Question

The number of ways in which thirty five apples can be distributed among $3$ boys so that each have any number of apples, is?

• A. $1332$
• B. $666$
• C. $333$
• D. None of these

Answer 1

The correct option is B

$666$

The explanation for the correct answer.

Find the number of ways.

Given: $\mathrm{n}=35,\mathrm{r}=3$

By positive integral formula, the number of ways $={}^{\mathrm{n}+\mathrm{r}-1}{\mathrm{C}}_{\mathrm{r}-1}$.

Therefore the required number of ways $={}^{37}{\mathrm{C}}_2$.

$$\begin{gathered} =\frac{37!}{2!\left(37-2\right)!}\left(\because {}^n{C}_r=\frac{n!}{r!\left(n-r\right)!}\right) \\ =\frac{37!}{2!\times 35!} \\ =\frac{37\times 36\times 35!}{2\times 35!} \\ =666 \end{gathered}$$

Hence option $\left(B\right)$ is the correct answer.