Question

Using the letters in the word ADDITION, find the number of permutations that can be formed using 3 letters at a time.

Answer 1

Answer: The number of permutations that can be formed using 3 letters of the word ADDITION at a time is 150.

Step-by-step explanation:

In the word ADDITION, we have 1-A’s, 2-D’s, 2-I’s, 1-N’s, 1-O’s, and 1-T’s. Thus, there are 6 distinct letters.

Case 1. When all the 3 letters are different

We can select 3 letters from 6 different letters of ADDITION and then arrange them in 3! Ways.

So,

The number of ways= 6C3*3!=6!/(3!*3!)*3!= 6*5*4= 120

Case 2. When 2 letters are same and one letter is distinct

The number of ways of forming 3 letter word having 2-same letters and 1 distinct =2C1*5C1*3!/2!

=2*5*3=30

So, the total number of permutations that can be formed using 3 letters at a time= 120+30=150

Answer 2

It's 336 don't listen to the other guy 150 isn't even an answer choice