How many different 4-letter words can be formed using the letters of the word "BANANA"?Choices:- 60 120 240 360

The word "BANANA" has 6 letters, but only 3 unique letters: B, N, and A.

Step 1: Count the number of each unique letter.

• B: 1
• N: 1
• A: 4

Step 2: Calculate the number of permutations of the word "BANANA" using the formula for permutations of a multiset: n! / (r1! * r2! * ... * rk!), where n is the total number of letters, and r1, r2, ..., rk are the counts of each unique letter.

• Total permutations of "BANANA": 6! / (1! * 1! * 4!) = 30

Step 3: However, we are only interested in 4-letter words. We have three cases to consider:

Case 1: All 4 letters are the same. This is not possible because we don't have any letter that appears 4 times.

Case 2: We have one letter that appears 3 times and one letter that appears once. This is possible only with the letter 'A'. We have 4 options for the position of the letter that appears once (B or N), so we have 4 * 2 = 8 words in this case.

Case 3: We have two letters that appear twice. This is possible with the letters 'A' and either 'B' or 'N'. We have 6 options for the positions of the two 'A's, and 2 options for the other letter, so we have 6 * 2 = 12 words in this case.

Adding up all the cases, we get 8 + 12 = 20 different 4-letter words that can be formed using the letters of the word "BANANA".

So, none of the given choices are correct.