Number of different words that can be formed from all letters of word $APPLICATION$ such that two vowels never come together is -
$(45)7!$
$8!$
$6!7!$
$(32)6!$
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?
$^{47}{C_4} + \mathop \sum \limits_{r = 1}^5 {}^{52 - r}{C_3} = $
If all the letters of the word $'GANGARAM'$ be arranged, then number of words in which exactly two vowels are together but no two $'G'$ occur together is-
How many words can be formed by taking $3$ consonants and $2$ vowels out of $5$ consonants and $4$ vowels
There were two women participating in a chess tournament. Every participant played two games with the other participants. The number of games that the men played between themselves proved to exceed by $66$ the number of games that the men played with the women. The number of participants is