In how many ways can the letters of a word 'G M A T I N S I G H T' be

Question

In how many ways can the letters of a word 'G M A T I N S I G H T' be arranged to form different words (whether the word makes sense or not) such that repeated letters appear together in the word i.e. two or more 'T' should appear together, two or more 'G's should appear together?

A) 11!
B) 9!
C) 8!
D) 11!/3!
E) 11!/(2!*2!*2!)

Source: https://www.GMATinsight.com

A) 11!
B) 9!
C) 8!
D) 11!/3!
E) 11!/(2!*2!*2!)

Source:  https://www.GMATinsight.com

broall · Answer

"GMATINSIGHT" has 1 A, 2 G(s), 1 M, 2 T(s), 2 I(s), 1 N, 1 S, 1 H. This word has totally 8 different characters.

Since repeated letters appear together, we just care about different letters. Now there are totally 8! different words. The answer is C

kayarat600 · Answer

I always solved as total numbers / combos what changed here?

DmitryFarberMPrep · Answer

Do you mean the factorials? As in something like answer choice E? The problem with that is that we aren't making groups. That would show how many ways to make 3 different 2-letter words, although in that case we'd also need to divide by 5! to cut the letters that aren't used. Here, we appear to be using all the letters in one word, so none of them are getting grouped separately. The repeated letters are just sticking together, so we can treat them the same as a single letter.

To be fair, though, this question isn't worded clearly enough. It just asks about forming "different words," so in theory the answer should be vastly larger. We'd have to look at all the 11-letter words, 10 letter words, 9 letters, etc. and add them all up.

In how many ways can the letters of a word 'G M A T I N S I G H T' be

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

In how many ways can the letters of a word 'G M A T I N S I G H T' be

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards