How many $2$-digit odd numbers can be formed from the digits $1, 2, 3, 4, 5$ and $8$,if repetition of digits is allowed?

In how many ways can a team of $11$ members be formed from a group of $15$ persons?

If $a$ denotes the number of permutations of $x + 2$ things taken all at a time,$b$ the number of permutations of $x$ things taken $11$ at a time,and $c$ the number of permutations of $x - 11$ things taken all at a time such that $a = 182bc$,then the value of $x$ is

$^nC_r \div ^nC_{r-1} = $

In a certain test,${a_i}$ students gave wrong answers to at least $i$ questions,where $i = 1, 2, 3, ..., k$. No student gave more than $k$ wrong answers. The total number of wrong answers given is:

If $n$ is even and the value of $^nC_r$ is maximum,then $r = $