If $C(n, 8) = C(n, 6)$,find $C(n, 2)$.

The number of words which can be formed from the letters of the word $MAXIMUM$,if two consonants cannot occur together,is

Find $\sum_{r=1}^{5} C(5, r)$

Out of $7$ consonants and $4$ vowels,how many words of $3$ consonants and $2$ vowels can be formed?

If the different permutations of the word $EXAMINATION$ are listed as in a dictionary,how many items are there in this list before the first word starting with $E?$

$A$ father with $8$ children takes them $3$ at a time to the Zoological gardens,as often as he can without taking the same $3$ children together more than once. The number of times each child will go to the garden is