If $x$ and $y$ are digits such that $17! = 355687428096000$, then $x+y$ equals

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

Among the inequalities below,which ones are true for all natural numbers $n > 1000$?
$I. n! \leq n^n$
$II. (n!)^2 \leq n^n$
$III. 10^n \leq n!$
$IV. n^n \leq (2n)!$

On her vacations,Veena visits four cities ($A, B, C$,and $D$) in a random order. What is the probability that she visits $A$ either first or second?

If all the numbers which are greater than $6000$ and less than $10000$ are formed with the digits $3, 5, 6, 7, 8$ without repetition of the digits,then the difference between the number of odd numbers and the number of even numbers among them is

The number of ways of distributing $15$ apples to three persons $A, B, C$ such that $A$ and $C$ each get at least $2$ apples and $B$ gets at most $5$ apples is