I have selected combination rule to solve this probability question. It calculates the amount of times where r number of objects can be taken from n number of objects irrespective of the order.
The combination formula is n(Cr= n!/(n-r)!r!
3 boys and 7 girls
(15c3 x30c7) all divided by 45c10
15c3 =15!/ [ (15-3) !3! ] equals 455 diverse ways of getting 3 boys from the 15 boys.
30c7=30 ! [ (30-7)! 7! ] equals 2035800 diverse ways of getting 7 girls from the 30 girls.
45c10 equals [45 !(45-10) !10! ] equals 3190187800 different ways of getting 10 students from 45 students.
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Getting the probability involves the multiplication of 3 boys combination by the 7 girls combination then divided by the total combination of students.
(455 x 2035800) ÷31901800= 0.29035568
So, the probability that precisely 3 lads will be nominated is about 0.29
