Question

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

Answer 1

in 8 ways
............

Answer 2

$\frac{8!}{2!}$ ways are there to arrange the letter of the word elephant.

• Here the concept is the permutation
• Number of all possible permutations of n things, taken r at a time
• = n!/(n-r)!
• The number of letters in the word elephant is 8.
• The number of repeating words is 2.
• The number of ways the letters of the word 'elephant' can be arranged

=  $\frac{n!}{(n-r)!}$

=$\frac{8!}{2!}$

Hence the letters of the word elephant can be arranged in $\frac{8!}{2!}$ ways