If $^{10}C_r = ^{10}C_{r+2}$,then $^5C_r$ 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} = $

If $^nC_r = 84$,$^nC_{r-1} = 36$,and $^nC_{r+1} = 126$,then $n$ equals:

$A$ person goes in for an examination in which there are four papers with a maximum of $m$ marks from each paper. The number of ways in which one can get $2m$ marks is

Three horses $H_{1}, H_{2}, H_{3}$ entered a field which has $7$ portions marked $P_{1}, P_{2}, P_{3}, P_{4}, P_{5}, P_{6}$ and $P_{7}$. If no $2$ horses are allowed to enter the same portion of the field,in how many ways can the horses graze the grass of the field?

How many words can be formed using the letters of the word $INSURANCE$,such that all vowels always come together?