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 such that each word starts with a "G" and ends with a "T" (whether the word makes sense or not)?

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

Source:  https://www.GMATinsight.com

maheshaero20 · Answer

Isn't the answer should be 9!/2!-1 ( since it is asking how many different words can be formed)

Eg: 
How many ways the letters of GMAT can be arranged. Ans: 4!
How many ways the letters of GMAT can be arranged to form different words. Ans: 4!-1 (We need to remove the word GMAT from the list, since it is already there)

philipssonicare · Answer

Explanation needed please!
I got 2·9! 2 Gs, 2 Ts and 9!/2! arrangements for the others

AbdulMalikVT · Answer

There are 11 letters. Two are fixed G and T. You are left with 9 letters. If all 9 were different then answer would have been 9!

There are 2 I. Then answer is 9!/2! ( once T is fixed at first or last, middle T can be treated as new one)

Suppose G and T can be fixed at first or last then it will be 9! / 2! X 2

Kinshook · Answer

First and last letters G & T are fixed. Only I is repeated in remaining 9 letters. Therefore, 9!/2!

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GMATinsight · Answer

G M A T I N S I G H T

Total Letters = 11

T used twice
I used twice
G used once
M used once
A used once
N used once
S used once
G used once
H used once

Gis fixed at first place and T is fixed at last place so the letters to be arranged = 11-2 = 9

Among those 9 letters there is one letter I repeated twice

Therefore total arrangements of 9 letters = 9!
the arrangements repeated due to swapping of identical letter 'I' = 2!

i.e. total desired outcomes = 9! / 2!

Answer: Option D

I hope this helps!!!

philipssonicare  .  maheshaero20

Eternal · Answer

Will use LOMO (lines, options, multiply, order) method here.

G  M   A   T   I   N   S   I   G   H  T

So after fixing G and T at the first place and the last place respectively, we have 9 lines i.e. we have to arrange 9 letter internally

That can be done in 9! ways.

Now in the nine letter I appears twice.
Does the order in which both I's can be written matters?
No, since I's are identical.

So we will divide the result by the no. of ways two I's can be arranged internally i.e. 2!

Hence the answer will be  \frac{9!}{2!}

Answer is (D)

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

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