Question

find the number of permutations in the word geometry

Answer 1

Puzzling answered 5 years ago
Well, if all the letters were different, then you'd have 8 choices for the first letter, 7 choices for the next, 6 choices for the third, etc.

So it looks like it should be 8!
= 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1
= 40,320 ways

However, the word GEOMETRY has a pair of repeated Es. There are two of them and their placement could be switched and it would still be the same word. So you need to divide by the ways to arrange 2 letters. This is 2! or just 2 x 1 = 2.

40,320 / 2
= 20,160 ways

Answer:
20,160 permutations of GEOMETRY