If ${}^{10}P_r = 604800$ and ${}^{10}C_r = 120$,then $r =$

$^{2n}C_4 : ^nC_3 = 99 : 4 \Rightarrow n = $

If $^{n}C_{8} = ^{n}C_{2}$,find $^{n}C_{2}$.

Let the number of elements in sets $A$ and $B$ be $5$ and $2$ respectively. Then the number of subsets of $A \times B$ each having at least $3$ and at most $6$ elements is:

$A$ father with $8$ children takes them $3$ at a time to the Zoological gardens,as often as he can without taking the same $3$ children together more than once. The number of times each child will go to the garden is

$A$ die is rolled three times. Find the probability of getting a larger number than the previous number each time.