Question

Find the number of arrangements of letters in the word CONSTITUTION that begin and end with N.

Answer 1

There are 12 letters in the word CONSTITUTION, in which ‘O’, ‘N’, ‘I’ repeat two times each, ‘T’ repeats 3 times.

When the arrangement starts and ends with ‘N’, other 10 letters can be arranged between two N, in which ‘O’ and ‘I’ repeat twice each and ‘T’ repeats 3 times.

∴ Required number of arrangements = \(\frac{10!}{2!2!3!}\)