How many different necklaces can be formed with $6$ white and $5$ red beads?

The number of ways in which one or more balls can be selected out of $10$ white,$9$ green,and $7$ blue balls are:

The number of circular permutations of $n$ different objects is

How many words can be made from the letters of the word $DELHI$,if $L$ comes in the middle in every word?

Each of the $10$ letters $A, H, I, M, O, T, U, V, W$ and $X$ appears the same when looked at in a mirror. They are called symmetric letters. Other letters in the alphabet are asymmetric letters. How many three-letter computer passwords can be formed (no repetition allowed) with at least one symmetric letter?

In how many different ways can the letters of the word '$THERAPY$' be arranged so that the vowels never come together?