Question

From a bag containing 5 nickels, 8 dimes, and 7 quarters, 5 coins are drawn at random and all at once. What is the probability of getting 2 nickels, 2 dimes, and 1 quarter?

Answer 1

Answer:

0.13

Step-by-step explanation:

From a bag containing 5 nickels, 8 dimes, and 7 quarters, 5 coins are drawn at random and all at once

we need to select 2 nickels from 5 nickels and select 2 dimes from 8 dimes and 1 quarter from 7 quarters

There are total of 5+8+7=20 coins

select 5 coins from total of 20 coins

2 nickels can be selected from 5 nickels in 5C2 ways

$5C2=\frac{5!}{2!(5-2)!} =\frac{5!}{2!(3!)!}=10$

2 dimes selected from 8 dimes

$8C2=\frac{8!}{2!(8-2)!} =\frac{6!}{2!(6!)}=28$

1 quarter selected from 7 quarter

$7C1=\frac{7!}{1!(7-1)!} =\frac{7!}{1!(6!)}=7$

5 coins selected from 20 coins

$20C5=\frac{20!}{5!(15)!} =15504$

probability of getting 2 nickels, 2 dimes, and 1 quarter

$\frac{10 \cdot 28 \cdot 7}{15504} =\frac{1960}{15504} =0.13$