All possible four-digit numbers are formed using the digits $0, 1, 2, 3$ such that no digit is repeated. The number of even numbers among them is

The number of different words that can be formed out of the letters of the word $MORADABAD$ taken four at a time is

There are $6$ men and $8$ women in a club,and a committee of $5$ people must be formed. What will be the number of ways to select $5$ people if only men are selected?

If $^{56}P_{r+6} : ^{54}P_{r+3} = 30800 : 1$,then $r = $

If $x, y$ and $r$ are positive integers, then $^x{C_r} + ^x{C_{r-1}} \cdot ^y{C_1} + ^x{C_{r-2}} \cdot ^y{C_2} + \dots + ^y{C_r} = $

There are three bags $B_1$,$B_2$,and $B_3$ containing $2$ Red and $3$ White,$5$ Red and $5$ White,and $3$ Red and $2$ White balls respectively. $A$ ball is drawn from bag $B_1$ and placed in bag $B_2$,then a ball is drawn from bag $B_2$ and placed in bag $B_3$,then a ball is drawn from bag $B_3$. The number of ways in which this process can be completed,if the same colour balls are used in the first and second transfers (Assume all balls to be different) is