Statistics
Step 2 of 2:How many different combinations of 4 movies can he rent if he wants at least two foreign films?
1170
Question Six: Victor is picking out some movies to rent, and he is primarily interested in foreign films and horror films. He has narrowed down his selections to 9 foreign films and 6 horror films. Step 1: How many different combinations of 4 movies can he rent?
1365
Possible outcomes:
(w-7 digits)*(x-8)*(y-8)*(z-8)= 7*8*8*8= 3584 possible outcomes
Question Twelve. At the grocery store, Mykel has narrowed down his selections to 5 vegetables, 5 fruits, 5 cheeses, and 5 whole grain breads. He wants to use the Express Lane, so he can only buy 15 items. In how many ways can he choose which 15 items to buy if he wants all 5 fruits?
C(5,5)*C(15,10)= Ans: 3003
Total number of different veggie wraps =
Number of vegetable choices * Number of condiment choices * Number of tortilla choices = 56 * 10 * 5 = 2800
Question Eleven. Karl wants to buy a new collar for each of his 2 cats. The collars come in a choice of 4 different colors. Step 1: How many selections of collars are possible if repetitions of colors are allowed?
4*4=16
Step 1. How many selections of collars are possible if repetitions of colors are allowed?
7*7*7 = 343
Step 3. Probability
= 1025/3584= 0.2860
No. Permutations P(9,9)
=362,880
Question Fourteen. How many ways can a person toss a coin 16 times so that the number of tails is between 9 and 13 inclusive?
Ans: 26196
Step 2: How many selections of collars are possible if repetitions of colors are not allowed?
P(4,2)= 12
Question Two: Consider all four-digit numbers that can be made from the digits 0-7 (assume that numbers cannot start with 0). What is the probability of choosing a random number from this group that is less than or equal to 3000? Enter a fraction or round your answer to 4 decimal places, if necessary.
Step 1: for digit number- w, x, y, z
No. different ways= 131560*362880
= 4.77 * 10^10
Step 2. Range between 1000-2777
=(w-2)*( x-8)*(y-8)*(z-8)= 1024 + 1( since <=3000)= 1025
Step 2. of 2: How many different combinations of 4 movies can he rent if he wants at least one horror film?
Ans: 36075
Question Eight. Lindsay is checking out books at the library, and she is primarily interested in mysteries and nonfiction. She has narrowed her selections down to eleven mysteries and ten nonfiction books. If she randomly chooses four books from her selections, what's the probability that they will all be mysteries? Enter a fraction or round your answer to 4decimal places, if necessary.
Ans: 0.0551
How many different combinations of 4 movies can he rent?
Ans: 40920
Question Nine. Consider all four-digit numbers that can be made from the digits 0-5 (assume that numbers cannot start with 0). What is the probability of choosing a random number from this group that is greater than 4000? Enter a fraction or round your answer to 4 decimal places, if necessary.
Ans; 0.4
Question Ten. An English teacher needs to pick 9 books to put on his reading list for the next school year, and he needs to plan the order in which they should be read. He has narrowed down his choices to 25 novels, 8 plays, and 21 nonfiction books. If he wants to include an equal number of novels, plays, and nonfiction books, how many different reading schedules are possible? Express your answer in scientific notation rounding to the hundredths place.
C(25,3)*C(8,3)*C(21,3) * P(9,9)= 6.216*10^13
Question Seven: A softball coach needs to choose 9 players to be in the batting lineup for the next game. There are 4 freshmen, 5 sophomores, 6 juniors, and 5 seniors on the team. How many ways can the batting order be chosen if the coach wants no more than 2 freshmen to be in the lineup?
C(4,0)*C(16,9)+C(4,1)*C(16,8)+C(4,2)*C(16,7)= 131 560
Question Five: At the grocery store, Wayne has narrowed down his selections to 7 vegetables, 8 fruits, 5 cheeses, and 5 whole grain breads. He wants to use the Express Lane, so he can only buy 15 items. In how many ways can he choose which 15 items to buy if he wants all 5 whole grain breads?
C(5,5)* C(20,10)= 184, 756
Question Four: If a coin is tossed 3 times, and then a standard six-sided die is rolled 2 times, and finally a group of two cards are drawn from a standard deck of 52 cards without replacement, how many different outcomes are possible?
C(52,2)*2^3*6^2=381, 888
Question Three: A veggie wrap at David's Deli is composed of 3 different vegetables and 2 different condiments wrapped up in a tortilla. If there are 8 vegetables, 5 condiments, and 5 types of tortilla available, how many different veggie wraps can be made?
C(8,3)*C(5,2)*C(5,1)
