Respuesta :
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
[tex]5C2=\frac{5!}{2!(5-2)!} =\frac{5!}{2!(3!)!}=10[/tex]
2 dimes selected from 8 dimes
[tex]8C2=\frac{8!}{2!(8-2)!} =\frac{6!}{2!(6!)}=28[/tex]
1 quarter selected from 7 quarter
[tex]7C1=\frac{7!}{1!(7-1)!} =\frac{7!}{1!(6!)}=7[/tex]
5 coins selected from 20 coins
[tex]20C5=\frac{20!}{5!(15)!} =15504[/tex]
probability of getting 2 nickels, 2 dimes, and 1 quarter
[tex]\frac{10 \cdot 28 \cdot 7}{15504} =\frac{1960}{15504} =0.13[/tex]
The probability of getting 2 nickels, 2 dimes, and 1 quarter is; 0.1264
We are given;
Number of nickels = 5
Number of dimes = 8
Number of quarters = 7
Total coins = 5 + 8 + 7
Total coins = 20
Number of ways of selecting 2 nickels will be;
N(2 nickels) = 5C2 = 10
Number of ways of selecting 2 dimes;
N(2 dimes) = 8C2 = 28
Number of ways of selecting 1 quarter;
N(1 quarter) = 7C1 = 7
Total number of ways of selecting 2 nickels, 2 dimes, and 1 quarter = 10 × 28 × 7 = 1960
Total number of coins selected out of the bag = 5
Thus;
Number of ways of selecting any 5 coins is;
N(any 5 coins) = 20C5 = 15504
Thus;
Probability of selecting 2 nickels, 2 dimes, and 1 quarter is; 1960/15504 = 0.1264
Read more on probability of selection at; https://brainly.com/question/251701
