Problem Solving

If the letters of the word A, F, T, E, R are permuted and arranged in a dictionary form like after, then for some (n > 2) how many other possible ways are there?
A. 119
B. 117
C. 88
Source is TestMagic. I dont have the OA

The Q is not very clear. What is n ?

5 letters an be arranged in 5! ways = 120 ways of which AFTER is one of them so 120-1=119.

I thought that they are asking for the number of all possible words that could appear after the word "AFTER" in the dictionary using letters A,F,T,E,R. The word should atleast be more than 2 characters in length. Let me know if this helps.

Can someone help with this question?

This question is poorly constructed so I'm struggling to give you a proper answer.

As has already been said, you have 119 x 5 letter combinations (discounting AFTER)

You have 5C4 * 4! 4 letter combinations (120)
You have 5C3 * 3! 3 letter combinations (60)
You have 5C2 * 2! 2 letter combinations (20)

= 119 + 120 + 60 + 20 = 319

I think you need to confirm the question wording

Either there is something wrong with the answer choices or with the question

Assuming n>2 meaning words with more than 2 alphabets need to be formed

Choosing 3: 5C3 * 3! = 60
Choosing 4: 5C4 * 4! = 120
Choosing 5 5C5 * 5! - 1(AFTER) = 119

Total = 60+120+119 = 299

I am not sure if i am right or not!!