Respuesta :
Answer:
The different amounts of money can the person give someone using 3 coins are {$0.16, $0.31, $0.36 and $0.40}.
Step-by-step explanation:
The four standard US coins are:
- Penny (P)
- Nickel (N)
- Dime (D)
- Quarter (Q)
The values of these coins in US dollars are as follows:
- 1 penny = $0.01
- 1 Nickel = $0.05
- 1 dime = $0.10
- 1 quarter = $0.25
Now it is said that a person has one coin of each type.
The person needs to give 3 coins to someone.
The number of ways in which he can select 3 coins from these 4 is:
[tex]{4\choose 3}=\frac{4!}{3!(4-3)!}=\frac{4\times 3!}{3!\times 1!}=4[/tex]
So there are 4 different ways to give 3 coins from 4.
The person can select 3 coins as follows:
{P, N, D}, {P, N, Q}, {P, D, Q} and {N, D, Q}
Compute the total amount of these selections as follows:
{P, N, D} = $0.01 + $0.05 + $0.10 = $0.16
{P, N, Q} = $0.01 + $0.05 + $0.25 = $0.31
{P, D, Q} = $0.01 + $0.10 + $0.25 = $0.36
{N, D, Q} = $0.05+ $0.10 + $0.25 = $0.40
Thus, the different amounts of money can the person give someone using 3 coins are {$0.16, $0.31, $0.36 and $0.40}.
