Porisma

Worked solution

Arrange MATHEMATICS by counting its repeated letters

In how many ways can the letters of the word MATHEMATICS be arranged?

CJC · Lecture · Self-Practice 1

Count the multiplicities

MATHEMATICS contains 11 letters:2 M,2 A,2 T, and one each of H,E,I,C,S. The multiplicities sum to 11.

How did this part go?

Apply the repeated-object formula

The count is 11!/(2! 2! 2!)=4,989,60011!/(2!\,2!\,2!)=4{,}989{,}600, matching the printed answer 4989600. The letter-count explanation supplements the source answer list.

How did this part go?

Common mistakes

Count both copies of each M,A,T. The other five letters each occur once.

Read the hint