How many words (with or without meaning) of $3$ distinct English alphabets can be formed?

In how many ways can a girl and a boy be selected from a group of $15$ boys and $8$ girls?

How many different words can be formed with the letters of the word '$BHARAT$'? In how many of these are $B$ and $H$ never together?

If $110$ triangles can be formed by joining $10$ points as vertices,in which $n$ points are collinear,then the value of $n$ is:

If the permutations of $A, B, C, D, E$ taken all together are written down in alphabetical order as in a dictionary and numbered,then the rank of the permutation $DEBAC$ is

If $C(n, 7) = C(n, 5)$,find $n$.