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

Number of ways ${=}^{37}{\mathrm{C}}_2=\frac{37!}{35!\times 2!}=666\text{ ways }$

For the distribution equation.

${\mathrm{x}}_1+{\mathrm{x}}_2+{\mathrm{x}}_3+\dots +{\mathrm{x}}_{\mathrm{r}}=\mathrm{n}$

The number of ways in which n things can be distributed among r in such a way each can receive none, one or more or all of n items are ${ }^{\mathrm{n}+\mathrm{r}-1}{\mathrm{C}}_{\mathrm{r}-1}$