How many words can be formed by taking two identical and two distinct letters from the letters of the word $COMBINATION$?

The number of four-lettered words that can be formed from the letters of the word $MAYANK$ such that both $A$'s are included but never together,is equal to:

The number of $7$-$digit$ numbers which are multiples of $11$ and are formed using all the digits $1, 2, 3, 4, 5, 7,$ and $9$ is

The total number of $5$-digit telephone numbers that can be formed such that at least one digit is repeated is .... (The first digit cannot be $0$).

If a number is chosen at random from the four-digit numbers formed by using the digits $0, 1, 2, 3, 4, 6$ without repetition,then the probability that it is divisible by $4$ is

The number of ways in which four letters of the word '$MATHEMATICS$' can be arranged is given by