A man has 12 coins that consist of 3 pennies, 4 nickels, and 5 quarters. How many distinct arrangements of thecoins can he make if he lays them in a row one at a time?
A) 27,720
B) 479,001,600
C) 9240
D) 83,160

Question

Quizplus · Accepted Answer

There are 12 coins, so there are 12! ways to arrange them. However, the coins of each type are indistinguishable, so we must divide by the number of permutations of each type. There are 3! ways to arrange the pennies, 4! ways to arrange the nickels, and 5! ways to arrange the quarters. Therefore, the number of distinct arrangements is 12! / (3! * 4! * 5!) = 27,720.

A Man Has 12 Coins That Consist of 3 Pennies