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

Accepted Solution

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 = 6no. of selections to be made = r = 3The order of selection of coins matter so we will use permutation here.Using the formula of Permutation:                   nPr = [tex]\frac{n!}{(n-r)!}[/tex]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 - nickelThey will count as two different cases.Calculating the no. of ways 3 coins can be selected from 6 coins.nPr = [tex]\frac{n!}{(n-r)!}[/tex] = [tex]\frac{6!}{(6-3)!}[/tex]nPr = 120