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
