$A$ box contains $2$ white balls,$3$ black balls,and $4$ red balls. In how many ways can $3$ balls be drawn from the box if at least one black ball is to be included in the draw?

Number of ways of arranging $8$ identical books into $4$ identical shelves where any number of shelves may remain empty is equal to

The number of elements in the set $\{x \in N : ^{20-2x}C_{x-3} \in N\}$ is

The least value of natural number $n$ satisfying $C(n, 5) + C(n, 6) > C(n + 1, 5)$ is

In how many ways can we select any $4$ letters from the word $CORGOO$?

In a shop,there are $5$ types of ice-creams available. $A$ child buys $6$ ice-creams.
$Statement-1$: The number of different ways the child can buy the $6$ ice-creams is $^{10}C_5$.
$Statement-2$: The number of different ways the child can buy the $6$ ice-creams is equal to the number of different ways of arranging $6$ $A$'s and $4$ $B$'s in a row.