Question

How many permutations of the letters of the word ‘APPLE’ are there?

Answer 1

Given: 

We have 5 letters 

To Find: Number of words formed with Letter of the word ‘APPLE.’ 

The formula used: The number of permutations of n objects, where p₁ objects are of one kind, p₂ are of the second kind, ..., p_k is of a kth kind and the rest if any, are of a different kind is = \(\frac{n!}{p_1!p_2! .....p_k!}\) 

‘APPLE’ consists of 5 letters out of which we have 2 Ps. 

Using the above formula 

Where, 

n = 5 

p₁ = 2 

\(\frac{5!}{2!}\) = 60

There are 60 permutations of the letters of the word ‘APPLE’.