Question

In how many ways can the letters of the word ‘CHEESE’ be arranged?

Answer 1

Given: We have 6 letters 

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

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 k^th kind and the rest if any, are of a different kind is = \(\frac{n!}{p_1!P_2! ......P_k!}\)

Suppose we have these words – C,H,E₁,E₂,S,E₃ 

Now if someone makes two words as CHE₁E₃SE₂ and CHE₂E₃SE₁

These two words are different because E₁, E₂ and E₃ are different but we have three similar E’s hence, in our case these arrangements will be a repetition of same words. 

In the word CHEESE, 3 E’s are similar 

∴ n = 6, p₁ = 3

\(\frac{6!}{3!}\) = \(\frac{720}{6}\) = 120

In 120 ways the letters of the word ‘CHEESE’ can be arranged.