The number of ways in which $10$ persons can go in two boats so that there may be $5 $ on each boat, supposing that two particular persons will not go in the same boat is
$\frac{1}{2}{(^{10}}{C_5})$
$2{(^8}{C_4})$
$\frac{1}{2}{(^8}{C_5})$
None of these
$^n{C_r} + {2^n}{C_{r - 1}}{ + ^n}{C_{r - 2}} = $
There are $12$ volleyball players in all in a college, out of which a team of $9$ players is to be formed. If the captain always remains the same, then in how many ways can the team be formed
A committee of $3$ persons is to be constituted from a group of $2$ men and $3$ women. In how many ways can this be done? How many of these committees would consist of $1$ man and $2$ women?
If the different permutations of all the letter of the word $\mathrm{EXAMINATION}$ are listed as in a dictionary, how many words are there in this list before the first word starting with $\mathrm{E}$ ?
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