SOLUTION: A class consists of 6 girls and 10 boys. If a committee of 3 is chosen at random from the class, find the probability that (i) 3 boys are selected, (ii) exactly 2 boys are selecte

Algebra ->  Permutations -> SOLUTION: A class consists of 6 girls and 10 boys. If a committee of 3 is chosen at random from the class, find the probability that (i) 3 boys are selected, (ii) exactly 2 boys are selecte      Log On


   

Question 551002: A class consists of 6 girls and 10 boys. If a committee of 3 is chosen at random from the class,
find the probability that (i) 3 boys are selected, (ii) exactly 2 boys are selected, (iii) at least one
boy is selected, (iv) exactly 2 girls are selected.
I want to know the answer to subsection (ii) and how it is different from subsection (i)
Answer by sudhanshu_kmr(1152) About Me  (Show Source):
You can put this solution on YOUR website!

Total number of possible committee = 16C3

i) number of possible committee having 3 boys = 10C3
probability = 10C3 /16C3

ii) number of possible committee having exactly 2 boys = 10C2* 6C1
probability = 10C2*6C1 /16C3


iii) number of possible committee having at least one boy = 16C3 - 6C3
probability = [ 16C3 - 6C3 ]/16C3



iv) number of possible committee having exactly 2 girls = 6C2* 10C1
probability = 6C2*10C1 /16C3


If any doubt, feel free to contact..