Question

​Twenty-three slips of paper are each marked with a different letter of the alphabet and placed in a basket. A slip is pulled​ out, its letter recorded​ (in the order in which the slip was​ drawn), and the slip is replaced. This is done 4 times. Find the probability that a word with no repetition of letters is formed.

The probability is ?

Answer 1

Given that 23 slips with 23 different letters from 26 letters of alphabet.

ANd given that repetition is not allowed. so that no two drawn should have save letter.

For first time (23 C 1) / (23 C 1)

For 2nd = (22 C 1) / (23 C 1) ==> Here letter what e got on first draw should not come. picked 23-1.

For 3rd = (21 C 1) / (23 C 1) ==> Previously picked 2 letters should not come.

for 4th , (20 C 1) / (23 C 1)

P(all diff lett) = 23*22*21*20/23^4 = 0.7594