The number of words not starting and ending with vowels formed, using all the letters of the word $'UNIVERSITY'$ such that all vowels are in alphabetical order, is
${}^8{C_4}.6!$
${}^8{C_4}.8!$
${}^8{C_6}.6!$
${}^8{C_4}.7!$
Two packs of $52$ cards are shuffled together. The number of ways in which a man can be dealt $26$ cards so that he does not get two cards of the same suit and same denomination is
If $^{20}{C_{n + 2}}{ = ^n}{C_{16}}$, then the value of $n$ is
How many words of $4$ consonants and $3$ vowels can be formed from $6$ consonants and $5$ vowels
A committee of $7$ has to be formed from $9$ boys and $4$ girls. In how many ways can this be done when the committee consists of:
at least $3$ girls?
The number of ways in which we can select three numbers from $1$ to $30$ so as to exclude every selection of all even numbers is