Ten students are participating in a race. In how many ways can the first $3$ prizes be won?

If the number of five-digit numbers with distinct digits and $2$ at the $10^{\text{th}}$ place is $336k$,then $k$ is equal to

$A$ five-digit number divisible by $3$ has to be formed using the numerals $0, 1, 2, 3, 4,$ and $5$ without repetition. The total number of ways in which this can be done is

If $n$ is even and the value of $^nC_r$ is maximum,then $r = $

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.

How many numbers greater than a million can be formed with the digits $2, 3, 0, 3, 4, 2, 3$?