Need help solving this combinatorics question

GRE Quant Problem Solving
1

Question: How many ‘4 letter words’ can be made from the word ‘BANANA’?

I know how to calculate total ways of arranging letters of a word with repeats, but how to go about solving this if the number of words are provided in the question, like in this case 4 letter word.

2

I think you asked this on Reddit?

3

  1. 3 A’s: There are 3 choices for the remaining letter, giving 4⋅3=124⋅3=12 cases

  2. 2 A’s: With 2 N’s, there are 6 cases, and with BN, SN, or SB we get 3⋅12=363⋅12=36 additional cases

  3. 1 A: with 2 N’s, we get 2⋅12=242⋅12=24 cases, and with NBS we get 4!=244!=24 additional cases

  4. 0 A’s: this gives 4⋅3=124⋅3=12 cases

Therefore the total is given by 12+42+48+12=11412+42+48+12=114 cases.