The least value of natural number $n$ satisfying $C(n,\,5) + C(n,\,6)\,\, > C(n + 1,\,5)$ is
$11$
$10$
$12$
$13$
If ${a_n} = \sum\limits_{r = 0}^n {} \frac{1}{{^n{C_r}}}$ then $\sum\limits_{r = 0}^n {} \frac{r}{{^n{C_r}}}$ equals
In the $13$ cricket players $4$ are bowlers, then how many ways can form a cricket team of $11$ players in which at least $2$ bowlers included
Out of $6$ boys and $4$ girls, a group of $7$ is to be formed. In how many ways can this be done if the group is to have a majority of boys
Number of different words that can be formed from all letters of word $APPLICATION$ such that two vowels never come together is -
How many $6 -$ digit numbers can be formed from the digits, $0,1,3,5,7$ and $9$ which are divisible by $10$ and no digit is repeated?