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

Question

A large pile of coins consists of pennies, nickels, dimes, and quarters. How many different collections of 30 coins can be chosen if there are at least 30 of each kind of coin? 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? If the pile contains only 20 dimes but at least 30 of each other kind of coin, how many collections of 30 coins can be chosen? If the pile contains only 15 quarters and only 20 dimes but at least 30 of each other kind of coin, how many collections of 30 coins can be chosen?

Explanation / Answer

a.

Since there is no restriction on how the coins are to be chosen ie how many of which type etc. we can simply look at total number of coins and count ways to choose 30 coins.

30 of each so total 120 coins. 30 coins can be chosen in:

C(120,30) ways

b.

15 of quarters 30 of each of other coinds so total 3*30+15 coins=105. 30 coins can be chosen in:

C(105,30) ways

c.

20 dimes and 30 of each of other coinds so total 20+3*30 coins=110. 30 coins can be chosen in:

C(110,30) ways

d.

15 quarters and 20 dimes and 30 each of other coins. So total:60+20+15=95 coins

So, 30 can be chosen in :

C(95,30) ways

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