Question

Determine whether each situation involves a permutation or a combination. Then find the number of possibilities: an arrangement of the letters in the word "intercept".

Answer 1

An arrangement of the letters in the word "intercept" is a permutation, as indicated by the word 'arrangement' indicating that reordering of the letters is required.
The 9! ways of rearranging the letters in INTERCEPT have to be divided by 2! and 2! because having fixed the positions of the non-repeated letters, the E's may be arranged in 2! ways and the T's in 2! ways without making a different word.
Therefore the number of permutations is given by
\[\frac{9!}{2!2!}\]