- #1

utkarshakash

Gold Member

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## Homework Statement

A word of 6 letters is formed from a set of 16 different letters of English alphabet(with replacement). Find out the probability that exactly two letters are repeated.

## Homework Equations

## The Attempt at a Solution

Total possible words = 26C16 . 16^6

Now there are 16C2 ways to choose two letters. Letter 1 can occur atleast twice and atmost 4 times. Same is the case with letter 2. So there arises 5 cases by which repetitions can occur.

Total words possible in these cases are (6C2.4C2.14.13+6C2.4C3.14+6C2.4C4+6C3.3C2.14+6C4.2C2)

∴n(P) = 26C16.16C2.(6C2.4C2.14.13+6C2.4C3.14+6C2.4C4+6C3.3C2.14+6C4.2C2)

P=n(S)/n(P)

But the answer which I get is incorrect.