The number of words from the letters of the word $'RAJASTHAN' $ by taking all the letters at a time in which vowels are alternate, are
$6! × ^7C_3$
$6 × 7!$
$5 × 6!$
$6 × 6!$
How many words of $4$ consonants and $3$ vowels can be formed from $6$ consonants and $5$ vowels
The number of $4$ letter words (with or without meaning) that can be formed from the eleven letters of the word $'EXAMINATION'$ is
The number of ways of dividing $52$ cards amongst four players equally, are
The number of words (with or without meaning) that can be formed from all the letters of the word $"LETTER"$ in which vowels never come together is
If $^n{C_r} = 84,{\;^n}{C_{r - 1}} = 36$ and $^n{C_{r + 1}} = 126$, then $n$ equals