1. ## Check Combinations

A large pile of coins consists of pennies, nickels, dimes and quarters.

a) How many different collections of 30 coins can be chosen if there are at least 30 of each kind of coin?
b) If the pile contains only 15 quarters but at least 30 of each other kind of coin, how many collections of 30 coins can be chosen?

2. ## Re: Check Combinations

Originally Posted by lovesmath
A large pile of coins consists of pennies, nickels, dimes and quarters.

a) How many different collections of 30 coins can be chosen if there are at least 30 of each kind of coin?
b) If the pile contains only 15 quarters but at least 30 of each other kind of coin, how many collections of 30 coins can be chosen?

answer to part a) is not C(30,4). it is C(33,3). it is equivalent to finding the number of non-negative integral solutions of x+y+z+w=30.

3. ## Re: Check Combinations

Is part (b) C(18,3) + C(33,3)?

4. ## Re: Check Combinations

Originally Posted by lovesmath
Is part (b) C(18,3) + C(33,3)?
the answer to part b) should obviously be less than the answer to part a).
my answer for part b) is C(33,3)-C(17,3)