1) A large pile of coins consists of pennies, nickels and quarters. If the pile

Question

1) A large pile of coins consists of pennies, nickels and quarters. If the pile contains only 12 quarters but at least 20 of each other kind of coin, how many collections of 20 coins can be chosen?

2) Consider a bag of jelly beans that has 30 red, 30 yellow, and 30 green jelly beans.

a) How many color combinations of 10 beans have at most three yellow beans?

b) How many color combinations of 10 beans have at least seven yellow beans?

3) Consider a class with 4 boys and 7 girls.

a) How many groups of six can be chosen that contain at most three women?

b) How many groups of six can be chosen that contain at least one man?

Explanation / Answer

The formula is C(k+n-1 k)

1.There are only 12 quarters, we have to subtract where we pick 12 quarters out from our possibility. For that , k is equal to 3(pennies,nickels and quarters),but n=12. Thus, there are C(3+20-1 3)-­C(3+12-1 3) ways.

hence the answer is: C(22 3)-C(14 3) ways.

2. a) It can have C(10+3-1 3)-C(6+3-1 3) combinations. It is C(12 3)-C(8 3).

b) at least 7 yellow beans means at least 7/10, or 8/10, or 9/10, or 10/10.

Hence answer is: C(10,7) + C(10,8) + C(10,9) + C(10,10)

3. a)Two groups

first group can contain two women and four men(total six)

second group can containg three women and three men(total six)

b) Five groups

first group can contain 1 man and 5 women(total six)

second group can contain 2 men and 4 women(tota six)

third group can contain 3men and 3 women(total six)

fourth group can contain 4men and 2 women(total six)

fifth group can contian 5men and 1 women(total six)

(Corrected the answer, pls give like)

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