Question

Find the number of permutations that can be made from the letters of the word ARRANGE.

(A). Do the words start with R?

(B). Do the words begin with N ?

Answer 1

We have,

The word ARRANGE

Part (A)

The word start with R

Then, permutation $=\frac{6!}{2}=\frac{6\times 5\times 4\times 3\times 2\times 1}{2}=360$ ways

Part (2)

The word start with N

$=\frac{6!}{2}\times 2!$

$=6!=6\times 5\times 4\times 3\times 2\times 1=720$ ways.