Question

If the number of arrangements of $4$ alike apples, $5$ alike mangoes, $1$ banana and $1$ orange in which all the apples are together or all the mangoes are together is $K$, then find the sum of digits in $K$.

Answer 1

No. of ways when Apples are together $+$ no. of ways when mangoes are together - No. of ways when Apples are also and Mangoes are also together
$\frac{8 !}{5 !}+\frac{7 !}{4 !}-4 ! $
$\Rightarrow k=522 \Rightarrow 9$