If $^{20}C_{n+2} = ^nC_{16}$,then the value of $n$ is

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.

The number of times the digit $3$ will be written when listing the integers from $1$ to $1000$ is

How many $3$-digit numbers can be formed by using the digits $1, 3, 6,$ and $8$,when the digits may be repeated any number of times?

In an election,the number of candidates is $1$ greater than the number of persons to be elected. If a voter can vote in $254$ ways,then the number of candidates is:

The number of four-digit numbers that can be formed using the digits $1, 2, 3, 4,$ and $5$ in which at least two digits are identical is