In how many ways can $n$ books be arranged in a row so that two specified books are not together?

In how many ways can a cricket team of $11$ players be selected out of $16$ players if $1$ particular player is to be excluded?

If a polygon has $44$ diagonals,then the number of its sides are

$A$ person wants to climb a $n$-step staircase using one step or two steps. Let $C_n$ denote the number of ways of climbing the $n$-step staircase. Then $C_{18} + C_{19}$ equals

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} = $

$3$ boys $B_1, B_2, B_3$ and $6$ girls $G_1, G_2, . . . , G_6$ are to be seated in a row. The number of ways they can be seated such that $B_1, B_2$ are separated and $G_1, G_2$ are also separated is equal to: