The number of distinct primes dividing $12! + 13! + 14!$ is

If $a + b + c = 50$ and $a, b, c$ are non-negative even integers,then the greatest value of $ab^2c$ is:

If the letters of the word $ATTEMPT$ are rearranged randomly,what is the probability that all $T$'s occur together?

The number of permutations of all the letters $AAAABBBC$ in which all the $A$'s appear together in a block of $4$ letters or all the $B$'s appear together in a block of $3$ letters,is-

Let $5$-digit numbers be constructed using the digits $0, 2, 3, 4, 7, 9$ with repetition allowed,and are arranged in ascending order with serial numbers. Then the serial number of the number $42923$ is $...............$.

The number of four-digit natural numbers which contain exactly two distinct digits is: