A boy needs to select five courses from $12$ available courses, out of which $5$ courses are language courses. If he can choose at most two language courses, then the number of ways he can choose five courses is
$454$
$465$
$546$
$645$
If $^{n} C_{8}=\,^{n} C_{2},$ find $^{n} C_{2}.$
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
Let $n(A) = 3, \,n(B) = 3$ (where $n(S)$ denotes number of elements in set $S$), then number of subsets of $(A \times B)$ having odd number of elements, is-
How many different words can be formed by jumbling the letters in the word $MISSISSIPPI$ in which no two $S$ are adjacent $?$
How many words of $4$ consonants and $3$ vowels can be formed from $6$ consonants and $5$ vowels