There is a group of $6$ boys and $4$ girls.
In how many ways can $3$ boys and $2$ girls be selected from a group of $6$ boys and $4$ girls?
A. $60$
B. $80$
C. $120$
D. $160$
I tried with $^nC_k$ but I couldn't do it. This is what I tried: $6!/3!*3!=20$
Best Answer
Essentially we are asking how many groups of $3$ boys from a pool of $6$ boys are there - answer $^6C_3=\frac{6!}{3!3!}=20$
Similarly, there $^4C_2=\frac{4!}{2!2!}=6$ possible groups of girls. Since these are independent, the total number is $20$ x $6$ $= 120$.
Answer = $120$.