In how many ways can a girl and a boy be selected from a group of $15$ boys and $10$ girls?

The correct option is A

$15\times 10$

Explanation for correct option:

Finding the required number of ways to select a girl and a boy:

Let's find the number of ways to select a boy

Number of boys $=15$

The number of ways a boys is selected out of $15$ boys $={}^{15}C_1$

$$\begin{gathered} =\frac{15!}{1!\times (15-1)!} \\ =15 \end{gathered}$$

Let's find the number of ways to select a girl

Number of girls $=10$

The number of ways a girl is selected out of $10$ girls $={}^{10}C_1$

$$\begin{gathered} =\frac{10!}{1!\times (10-1)!} \\ =10 \end{gathered}$$

The total number of ways a girl and a boy can be selected from a group of $15$ boys and $10$ girls$=15\times 10$

Hence, option (A) is correct.