A large pile of coins consists of pennies nickels dimes and

A large pile of coins consists of pennies, nickels, dimes, and quarters (at least 20 of each). (a) How many different collections of 20 coins can be chosen? (b) How many different collections of 20 coins chosen at random will contain at least 3 coins of each type? (c) What is the probability that a collection of 20 coins chosen at random will contain at least 3 coins of each type?

Solution

a)
4 ways of choosing each coin, so
4*4*......20 times
= 4^20 ways


b )
at least 3 of each coin means 12 are pre-determined, leaving 8 to be allocated in
4^8 ways


c )
using results from qa & qb,
reqd. probability =
4^8 / 4^20
= 1/4^12