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6 different letters of an alphabet are given. Words with four letters are formed from these given letters. Determine the number of words which have at least one letter repeated. 

(a) 1296 

(b) 996 

(c) 936 

(d) 360

1 Answer

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Best answer

(c) 936

The number of 4-letter words which can be formed from 6 letters when one or more of the letters is repeated = 6 × 6 × 6 × 6 = 1296 

Number of 4-letter words which can be formed from the given 6 letters when none of the letters is repeated 

= Number of arrangements of 6 letters taken 4 at a time 

= 6P4 = \(\frac{6!}{(6-4)!} = \frac{6!}{2!}\) = 6 × 5 × 4 × 3 = 360 

∴ Number of 4 letter words which have at least one of their letters repeated = 1296 – 360 = 936.

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