Total number of distinct 4 letters words that can be formed from the letters of the word NANDINI', so that at most 2 alike letters are together, is
Answers
total of ways in which 4 letter word can be made out of the word
NANDINI: 1680+756+18 = 2454
Answer:
There are 174 ways to arrange the letters of of the word NANDINI', so that at most 2 alike letters are together.
Step-by-step explanation:
The word is NANDINI = N, A, D, I
Therefore, we have 4 distinct letters and 2 alike words
We need to form a 4 letter word such that at most 2 alike letters are together.
There are following cases that are possible:
Case 1 : Both pairs are alike
We can choose one out of the two alike pair in ²C₂ ways
The word formed can be arranged in 4! ways
As there are two pairs that has two repetitive letters, we will divide it by 2! * 2!
Therefore total number of ways = ²C₂ *4!/(2!*2!) = 1 *4!/2*2 = 6 ways
Case 2 : One pair is alike and two distinct letters
We can choose one out of the two alike pair in ²C₁ ways
and two distinct letters in ⁴C₂ ways.
The word formed can be arranged in 4! ways
As there is one pair that has two repetitive letters, we will divide it by 2!
Therefore total number of ways = ²C₁ * ⁴C₂*4!/2! = 2 * 6*24/2 = 144 ways
Case 3 : All letters distinct
As we have 4 distinct letters, we can arrange them in 4! ways.
4! = 24 ways
Therefore, the total number of ways = 6 + 144 + 24
= 174 ways
Hence, there are 174 ways to arrange the letters of of the word NANDINI', so that at most 2 alike letters are together.