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 o

Question

3 months ago

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f getting 2 nickels, 2 dimes, and 1 quarter?

1 answer:

Svet_ta [12.7K] · Answer 1 · 2026-02-24T11:04:35+03:00

Answer:

0.13

Detailed explanation:

In a bag containing 5 nickels, 8 dimes, and 7 quarters, we randomly select 5 coins at once.

This means we need to pick 2 nickels from the 5 available, 2 dimes from the 8, and 1 quarter from the 7 quarters.

In total, there are 5 + 8 + 7 = 20 coins.

Selecting 5 coins from the entire set of 20 coins.

2 nickels can be chosen from 5 in 5C2 ways.

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

2 dimes can be taken from 8.

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

1 quarter from 7 quarters.

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

5 coins chosen from 20.

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

The probability of obtaining 2 nickels, 2 dimes, and 1 quarter is given by:

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