Question

Jason has five coins in his pocket: a penny, a nickel, a dime, a quarter, and a half-dollar. How many different sums of money can be formed using exactly three of the coins?

Answer 1

Answer:  10

Step-by-step explanation:

Given : Jason has five coins in his pocket: a penny, a nickel, a dime, a quarter, and a half-dollar.

Since each coin has different value from others.

So the combination of any 3 coin will give a different amount.

We know that the combination of r things out of n things = $^nC_r=\dfrac{n!}{r!(n-r)!}$

Therefore , the combination of 3 coins out of 5 = $^5C_3=\dfrac{5!}{3!(5-3)!}=\dfrac{5\times4\times3!}{3!\times2!}=10$

Hence, the number of different sums of money can be formed using exactly three of the coins = 10