MAT 121 Test 1
At a lumber company, shelves are sold in 4 types of wood, 5 different widths and 5 different lengths. How many different types of shelves could be ordered?
100
Find the number of distinguishable arrangements of the letters of the word TRILLION
10080
If you toss 10 fair coins, in how many ways can you obtain at least two tails?
1013
After rolling the first ball of a frame in a game of 10-pin bowling, how many different pin configurations can remain (assuming all configurations are physically possible)?
1024
If you roll two fair dice (one black die and one white die), in how many ways can you obtain a 4 on at least one die?
11
At a wedding reception, the bride and groom and three attendants will form a receiving line. How many ways can they be arranged in each of following cases? B) The bride and groom must be the last two in line.
12
Given a group of students: G={Allen, Brenda, Chad, Dorothy, Eric}, count the number of different ways of choosing a treasurer and a secretary if the two must not be the same sex.
12
How many ways can a male and a female be selected to decorate for a party from a club consisting of eight members where six are men and two are women?
12
A student is told to work any 7 out of 10 questions on an exam. In how many different ways can he complete the exam? (The correctness of his answers has no bearing.) Round the answer to the nearest whole number.
120
Amy, Brenda, Chuck, Deirdre, and Early have reserved five seats in a row at the theater, starting at an aisle seat. In how many ways can they arrange themselves?
120
At a wedding reception, the bride and groom and three attendants will form a receiving line. How many ways can they be arranged in each of following cases? A) Any order will do.
120
Tonya's ZIP code is 14768. How many zip codes altogether could be formed, each one using those same five digits?
120
A committee of six Congressmen will be selected from a group of ten Republicans and five Democrats. Find the number of ways of obtaining a committee with exactly three Republicans.
1200
Find the number of combinations (subsets) of 9 things taken 5 at a time.
126
How many ways can a teacher give six different prizes to six of her 25 students?
127512000
Find the number of ways to get the following card combinations from a 52-card deck. All clubs in a five-card hand
1287
Four accounting majors, two economics majors, and three marketing majors have interviewed for five different positions with a large company. Find the number of different ways that five of these people could be hired if the first two positions are to be filled by accounting majors, the third position is to be filled by an economics major, and the last two positions are to be filled by marketing majors.
144
Six men and six women have just six tickets in one row to the theater. In how many ways can they sit if the first person in the row is a woman, and the people alternate woman, man, woman, man, and so on?
14400
If you toss four fair coins, in how many ways can you obtain at least one head?
15
A panel containing four on-off switches in a row is to be set. Assuming no restrictions on individual switches, use the fundamental counting principle to find the total number of possible panel settings.
16
If a single card is drawn from a standard 52-card deck, in how many ways could it be an ace or a spade?
16
Betty's collection of twelve albums includes one jazz album. Betty will choose four of her albums to play on a road trip. (Assume order is not important.) C) How many of them would include the jazz album?
165
For $3.98 you can get a salad, main course, and dessert at the cafeteria. If you have a choice of 4 different salads, 7 different main courses, and 6 different desserts, then how many different meals can you get for $3.98?
168
Determine the number of permutations (arrangements) possible of 7 things taken 3 at a time.
210
In a race in which seven automobiles are entered and there are no ties, in how many ways can the first three finishers come in?
210
Don has eight pairs of shoes, nine pairs of pants, and three shirts. If all items are compatible, how many different outfits can he wear?
216
When two fair dice are rolled, there are 36 possible outcomes. How many possible outcomes would there be if three fair dice were rolled?
216
If a single card is drawn from a standard 52-card deck, in how many ways could it be a diamond or a face card?
22
To win at LOTTO in one state, one must correctly select 5 numbers from a collection of 51 numbers (1 through 51). The order in which the selection is made does not matter. How many different selections are possible?
2349060
Counting numbers are to be formed using only the digits 6, 4, 1, 3, and 5. Determine the number of different possibilities for two-digit numbers.
25
How many different ways could three distinct days of the week be chosen so that at least one of them begins with the letter Upper T?
25
A musician plans to perform 5 selections for a concert. If he can choose from 7 different selections, how many ways can he arrange his program? Round the answer to the nearest whole number.
2520
If two fair dice, one red and one white, are rolled, in how many ways can the result be obtained? The sum of the two dice is at least 6.
26
If a single card is drawn from a standard 52-card deck, in how many ways could it be either a red card or an ace?
28
A committee of six Congressmen will be selected from a group of six Democrats and five Republicans. Find the number of ways of obtaining exactly one Republican.
30
If two fair dice, one red and one white, are rolled, in how many ways can the result be obtained? A different number on each die.
30
If you toss five fair coins, in how many ways can you obtain at least one head?
31
Betty's collection of twelve albums includes one jazz album. Betty will choose four of her albums to play on a road trip. (Assume order is not important.) B) How many of these sets would not include the jazz album?
330
In a race in which eight automobiles are entered and there are no ties, in how many ways can the first three finishers come in?
336
If you roll two fair dice (one black die and one white die), in how many ways can you obtain a sum of at least 3?
35
A sports shop sells tennis rackets in 4 different weights, 3 types of string, and 3 grip sizes. How many different rackets could they sell?
36
In how many ways could members of the following club line up all 9 members for a photograph? (James, Sandy, Jane, Alan, Tammy, Cathy, David, Sandy Ashley)
362880
Four married couples have reserved eight seats in a row at the theater, starting at an aisle seat. In how many ways can they arrange themselves if no couple is to be separated?
384
If a single card is drawn from a standard 52-card deck, in how many ways can a card other than a face card be obtained?
40
How many two-digit counting numbers are not multiples of 2?
45
Find the number of ways to get the following card combinations from a 52-card deck. Two red jacks and two black queens
48
Betty's collection of twelve albums includes one jazz album. Betty will choose four of her albums to play on a road trip. (Assume order is not important.) A) How many different sets of four albums could she choose?
495
There are 12 members on a board of directors. If they must form a subcommittee of 4 members, how many different subcommittees are possible?
495
If you toss 9 fair coins, in how many ways can you obtain at least two heads?
502
An electronics store receives a shipment of 40 graphing calculators, including 4 that are defective. Four of the calculators are selected to be sent to a local high school. How many of these selections will contain no defective calculators?
58905
At a wedding reception, the bride and groom and three attendants will form a receiving line. How many ways can they be arranged in each of following cases? C) The groom must be last in line with the bride next to him.
6
Find the number of different three-member committees that could be selected from the group of {Mary, Norman, Paula, Raymond, Sally} given that Sally must be on the committee.
6
If two fair dice, one red and one white, are rolled, in how many ways can the result be obtained? The sum of the two dice is less than 5.
6
How many different three-digit numbers can be written using digits from the set {1, 2, 3, 4, 5} without any repeating digits?
60
A multiple-choice test consists of 8 questions with each question having 3 possible answers. How many different ways are there to mark the answers?
6561
Find the number of ways to get the following card combinations from a 52-card deck. No face cards in a five-card hand
658008
A group of five entertainers will be selected from a group of twenty entertainers that includes Small and Trout. In how many ways could the group of five include at least one of the entertainers Small and Trout? (Small is one, Trout is another)
6936
Four accounting majors, two economics majors, and three marketing majors have interviewed for five different positions with a large company. Find the number of different ways that five of these people could be hired if the first position is to be filled by an accounting major, the second position is to be filled by an economics major, the third position is to be filled by a marketing major, and the last two positions can be filled by any major.
720
A pool of possible jurors consists of 11 men and 13 women. How many different juries consisting of 5 men and 7 women are possible?
792792
Suppose that 9 fair coins are tossed. Find the numbers of ways of obtaining exactly 6 heads. Round the answer to the nearest whole number.
84
Given a committee of 8 women and 11 men, count the number of different ways of choosing a president, a secretary, and a treasurer, if the president must be a woman and the secretary and treasurer must be men. Assume no one can hold more than one office.
880
How many ways can a president and vice-president be chosen from a committee of 10 people?
90
A contractor builds homes of 11 different models and presently has 3 lots to build on. In how many different ways can he arrange homes on these lots? Assume 3 different models will be built.
990
Consider the selection of a thirteen card bridge hand. Is this a combination, a permutation, or neither?
combination
Determine whether the object is a permutation or a combination. a hand of cards in poker
combination
Among the 2,598,960 possible 5-card poker hands from a standard 52-card deck, how many contain at least one face card?
complement of no face cards 1940952
Among the 2,598,960 possible 5-card poker hands from a standard 52-card deck, how many contain at least one queen?
complement of no queens 886656
Determine whether the object is a permutation or a combination. an automobile license plate number
neither
Determine whether the object is a permutation or a combination. a 10-digit telephone number (including area code)
neither
Consider the arrangements of the letters in the word ALGEBRA. Is this a combination, a permutation, or neither?
permutation
Consider the selection of officers for a club. Is this a combination, a permutation, or neither?
permutation
Determine whether the object is a permutation or a combination. the batting order for a baseball team
permutation
