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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?

Sagot :

oladayoademosu

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

Number of ways of selecting 3 students out of the total

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.

Number of ways of selecting 3 girls out of 14

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

Probability of all girls

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:

https://brainly.com/question/24756209

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