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Nitella
1 month ago
12

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

f getting 2 nickels, 2 dimes, and 1 quarter?
Mathematics
1 answer:
Svet_ta [12.7K]1 month ago
5 0

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

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