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Andrei [34K]
2 years ago
6

Mr. Ramsey has 14 girls and 10 boys in her class she will randomly create one group of three students to work on a project what

is a probability that the group will be all girls?
Mathematics
1 answer:
Mrrafil [7]2 years ago
4 0

The probability that the group will be all girls is 91/506

<h3 /><h3>Number of ways of selecting 3 students out of the total</h3>

Since there are 14 girls and 10 boys, the total number of students is 10 + 14 = 24.

So, the total number of ways of selecting 3 students from 24 is ²⁴C₃.

<h3 /><h3>Number of ways of selecting 3 girls out of 14</h3>

Also, the total number of ways of selecting a group of 3 of all girls out of the 14 girls is ¹⁴C₃ = 14

<h3 /><h3>Probability of all girls</h3>

So, the probability of selecting a group of 3 of all girls = number of ways of selecting 3 girls/total number of selections = ¹⁴C₃ ÷ ²⁴C₃

= 14 × 13 × 12/3! ÷ 24 × 23 × 22/3!

= 7 × 13/23 × 22

= 91/506

So, the probability that the group will be all girls is 91/506

Learn more about probability here:

brainly.com/question/24756209

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