Eight different letters of an alphabet are given. Words of 4 letters f

1.	Eight different letters of an alphabet are given. Words of 4 letters from these are formed. Find the number of such words with at least one letter repeated.
Answer» If any letter can be used any number of times, then the number of words of 4 Letters with 8 different letters is 8 × 8 × 8 × 8 = 8⁴ = 4096 Number of words of 4 letters with at least one letter repetition not allowed = ⁸P₄ = 8 × 7 × 6 × 5 = 1680 ∴ Number of 4 letter words with at least one letter repeated is 8⁴ – ⁸P₄ = 4096 – 1680 = 2416.

Eight different letters of an alphabet are given. Words of 4 letters from these are formed. Find the number of such words with at least one letter repeated.

Answer»

If any letter can be used any number of times, then the number of words of 4 Letters with 8 different letters is 8 × 8 × 8 × 8 = 8⁴ = 4096

Number of words of 4 letters with at least one letter repetition not allowed = ⁸P₄ = 8 × 7 × 6 × 5 = 1680

∴ Number of 4 letter words with at least one letter repeated is 8⁴ – ⁸P₄ = 4096 – 1680 = 2416.