Calculate how many different sequences can be formed that us

Calculate how many different sequences can be formed that use all of the letters of the word mathematics, as an example aacheimmstt is one such sequence. Please show all work and explain your methods.

Solution

M A T H E M A T I C S

number of letters = 11

so number of sequence formed = 11! /(2! x 2! x 2!)

in te denominator its divided 3 times by 2 factorial because m appears 2 times, a appears 2 times and t appears 2 times.