Test 2

The TU Bakery sells only six kinds of cookies: peanut butter, raisin, oatmeal, chocolate, lemon, and sugar. How many different combinations of 13 cookies can you buy if you do not buy any oatmeal cookies, and buy exactly 4 raisin cookies?

C(12,3)

How many 16-bit strings have exactly five 1's?

C(16,5)

In how many ways can a committee of six persons be selected from seven men and nine women such that at least one man and at least one women is on the committee?

C(16,6)-C(7,6)-C(9,6)

In how many ways can a committee of five persons be selected from eight men and nine women, such that at least one man and at least one women is on the committee?

C(17,5)-C(8,5)-C(9,5)

In how many ways can 20 identical books be distributed among 6 students?

C(25,5)

An exam has 10 questions. How many ways can (integer) points be assigned to the problems if the total points in 150 and each problems is worth at least ten points each?

C(59,9)

In how many different ways can 10 identical books be distributed to three students such that each student receives at least two books?

C(6,2)

20 different gifts are on a table. How many ways can they be distributed to five children such that each child receives four gifts?

(20!)/([4!]^5)

In how many ways can 4 different Math books, 6 different History books, 7 different Physics books and 5 different English books be arranged on a shelf such that all books of the same subject are together?

4![4!*6!*7!*5!]

Determine how many strings can be formed by ordering the letters ABCDE such that C appears before A.

60

How many balls must be chosen from among 18 red balls, 22 green balls, 17 yellow balls, and 21 blue balls in order to guarantee that at least 9 balls of the same color are chosen?

9+8+8+8=33

In how many ways can a committee consisting of five women and seven men be chosen from a group of ten women and twelve men?

C(10,5)*C(12,7)

Consider 10 people (P1, P2, .. P10). How many 6 member teams can be formed that do not contain P2 and P8?

C(10,6)-C(8,4)

In how many different ways can 12 identical books be distributed to four students such that each student receives at least one book?

C(11,3)

Consider 11 people (P1, P2, .. , P11). How many 6-member teams can be formed that do not contain both P4 and P8?

C(11,6)-C(9,4)

A Bakery sells only six kinds of cookies: peanut butter, raisin, oatmeal, chocolate, lemon, and sugar. How many different combinations of 12 cookies can you buy if you do not buy any sugar cookies, and buy exactly 3 raisin cookies?

C(12,3)

How many three-digit numbers can be formed from the following seven digits? 1, 2, 3, 4, 5, 6, 7? THE DIGITS ARE NOT REPLACED

P(7,3)

An agency has 11 available foster families, F1, F2, .. F11, and 6 children, C1, C2, .. C6, to place. If no family can get more than one child, in how many ways can the children be placed?

P(11,6)

In how many ways can 12 identical Math books and 2 different History books be arranged on a shelf such that the History books are not next to each other?

P(13,2)

In how many ways can 14 identical Math books and 2 different Art books be arranged on a shelf such that the Art books are not next to each other?

P(15,2)

Given 15 people, we are to select a committee of 6 persons such that one person is President, one person is Treasurer, and the 4 other committee members have no special duties. In how many ways can this be done?

P(15,2)*C(13,4)

How many routes are there in the ordinary xy-coordinate system from origin to the point (9,4), if we limited to steps of one unit in the positive x-direction and one unit in the y-direction?

(13!)/[9!4!]

How many 12-bit strings end with 11001 or 011?

(2^7)+(2^9)

Given 7 identical red balls, and 13 identical blue balls, how many different arrangements of the 20 balls are there in which all 7 red balls are together, and all 13 blue balls are together?

2 ways

In how many ways can 3 different Math books, 5 different History books, 8 different Physics books and 6 different English books be arranged on a shelf such that all books of the same subject are together?

4![3!*5!*8!*6!]

How many positive integers less than 1,000 are such that the sum of their digits is 6/

C(8,2)

How many 10-bit strings are there containing three 0's and seven 1's with no consecutive 0's?

C(8,3)

How many positive integers less than 10,000 are such that the sum of their digits is 5?

C(8,3)

In how many ways can a committee of eight persons be formed from a group of nine men and ten women, such that the number of women on the committee is three times the number of men on the committee?

C(9,2)*C(10,6)

Consider a group of 6 men and 8 women. From this group 3 persons are to be selected to be President, Secretary, and Treasurer of the group. How many ways can this be done if: a) Any person may be selected for the offices? b) One man and two women must be selected? c) At least one man, and at least one women is selected?

a) P(14,3) b) [C(6,1)*C(8,2)]3! c) P(14,3)-P(6,3)-P(8,3)

Consider a group of 6 men and 9 women. From this group 3 persons are to be elected to be President, Secretary, and Treasurer of the group. In how many ways can this be done: a) One man and two women must be selected? b) At least one man, and at least one women is selected?

a) [C(6,1)*C(9,2)]3! b) P(15,3)-P(6,3)-P(9,3)