Let $A_1,A_2,........A_{11}$ are players in a team with their T-shirts numbered $1,2,.....11$. Hundred gold coins were won by the team in the final match of the series. These coins is to be distributed among the players such that each player gets atleast one coin more than the number on his T-shirt but captain and vice captain get atleast $5$ and $3$ coins respectively more than the number on their respective T-shirts, then in how many different ways these coins can be distributed ?

What is the number of ways of choosing $4$ cards from a pack of $52$ playing cards? In how many of these

four cards are of the same suit,

If $^n{C_r} = {\,^n}{C_{r - 1}}$ and $^n{P_r}{ = ^n}{P_{r + 1}}$, then the value of $n$ is

If all the letters of the word $'GANGARAM'$ be arranged, then number of words in which exactly two vowels are together but no two $'G'$ occur together is-

The number of ways, $16$ identical cubes, of which $11$ are blue and rest are red, can be placed in a row so that between any two red cubes there should be at least $2$ blue cubes, is

The value of $^{15}{C_3}{ + ^{15}}{C_{13}}$ is