Question

2. How many more possible arrangements can be made using the letters of the word PERMUTATIONS than using the letters of the word COMBINATIONS? Justify your answer.

Answer 1

PERMUTATIONS -
`(12!)/(2!)`

COMBINATIONS -
`(12!)/(2!2!)`

`((12!)/(2!))/((12!)/(2!2!))=(12!)/(2!)\cdot(2!2!)/(12!)=2!=2`