# A class consists of $10$ boys and $8$ girls.Three students are selected at random.Find the probability that the selected row has

$(a)All\;boys \quad (b)All\;girls \quad (c)2\;boys\;and\;1\;girl\quad$

Toolbox:
• In any problem that involves determining the outcomes, we can write down the sample space and count the number of favorable outcomes.
• $P(A)=\large\frac{n(A)}{n(s)}$
Step 1:
(a)No of boys in the class=$10$
No of students selected =3
Samle space $n(s)=18C_3$
No of boy selected is that all are boys $n(A)=10C_3$
$\therefore$ the probability that all are boys $P(A)=\large\frac{n(A)}{n(S)}$
$\Rightarrow \large\frac{10C_3}{18C_3}$
Step 2:
(b) No of girls in the class =8
No of students selected=3
No of girl selected is that all are girlss $n(B)=8C_3$
$\therefore$ the probability that all are girls $P(B)=\large\frac{n(B)}{n(S)}$
$\Rightarrow \large\frac{8C_3}{18C_3}$
Step 3:
(c) The probability that 2 boys and 1 girl is selected to be $\large\frac{n(C)}{n(S)}$
$\Rightarrow \large\frac{10C_3\times 8C_3}{18C_3}$