Question

How many ways can a person select 3 coins from a box consisting of a penny, a nickel, a dime, a quarter, a half dollar, and a one dollar coin? The order of coins is important

Answer 1

Answer:

A person can select 3 coins from a box containing 6 different coins in 120 different ways.

Step-by-step explanation:

Total choices = n = 6

no. of selections to be made = r = 3

The order of selection of coins matter so we will use permutation here.

Using the formula of Permutation:

                  nPr = $\frac{n!}{(n-r)!}$

We can find all possible ways arranging 'r' number of objects from a given 'n' number of choices.

Order of coin is important means that if we select 3 coins in these two orders:

--> nickel - dime - quarter

--> dime - quarter - nickel

They will count as two different cases.

Calculating the no. of ways 3 coins can be selected from 6 coins.

nPr = $\frac{n!}{(n-r)!}$ = $\frac{6!}{(6-3)!}$

nPr = 120