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

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- 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 $\large\frac{n(C)}{n(S)}$

$\Rightarrow \large\frac{10C_3\times 8C_3}{18C_3}$

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