The number of ways in which 21 identical apples can be distributed...

Let us initially distribute $2$ apples to each children.

So, the remaining $15$ apples are to be distributed such that each children can get any number of apples.

So, the required number of ways will be given by $N = Cr - 1 n + r - 1$.

$⇒ N = C2 15 + 3 - 1$

$⇒ N = C2 17$

$⇒ N = \dfrac{17 \times 16}{2}$

$⇒ N = 136$