Question

How many seven–letter permutations can be formed from the letters of the word GIGGLES?

Answer 1

840

Explanation:

The answer is the same as that of the other contributions, but I would like to explain a little more how the calculations are obtained.

The number of ways an n-element set can be ordered is:

`P_n = n !`

as long as the elements are different from each other.

But suppose the first element is repeated `a` times. Then, since all the repeats of the first element are indistinguishable from each other, in reality they will only have:

`{n !}/{a !}`

possible ordinations.

Finally, if the rest of the elements of the set can also be repeated a number of times each, i.e. we have `b` second elements, `c` third, etc., then we have:

`P_{n (a, b, c...)} = {n!}/{a! cdot b! cdot c! cdot ...}`

possibilities of ordering said set of elements.