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 - $\dfrac{12!}{2!}$

COMBINATIONS - $\dfrac{12!}{2!2!}$

$\dfrac{\dfrac{12!}{2!}}{\dfrac{12!}{2!2!}}=\dfrac{12!}{2!}\cdot\dfrac{2!2!}{12!}=2!=2$