If $^n{C_3} + {\,^n}{C_4} > {\,^{n + 1}}{C_3},$ then
$n > 6$
$n > 7$
$n < 6$
None of these
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
How many words of $4$ consonants and $3$ vowels can be formed from $6$ consonants and $5$ vowels
Consider $4$ boxes, where each box contains $3$ red balls and $2$ blue balls. Assume that all $20$ balls are distinct. In how many different ways can $10$ balls be chosen from these $4$ boxes so that from each box at least one red ball and one blue ball are chosen?
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
The number of ways in which five identical balls can be distributed among ten identical boxes such that no box contains more than one ball, is