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 vowels occupy the odd numbered positions in the word (whether the word makes sense or not)?

A) 11!
B) 15*8!
C) 8!
D) 8!/(2!*2!)
E) 11!/(2!*2!*2!)

Source: https://www.GMATinsight.com

A) 11!
B) 15*8!
C) 8!
D) 8!/(2!*2!)
E) 11!/(2!*2!*2!)

Source:  https://www.GMATinsight.com

ganand · Answer

Hi,

Word is 'G M A T I N S I G H T'
Total positions = 11 
Odd positions = 6 ,Vowels: A, I, I 
Repetitive letters: G - 2, T - 2, I - 2,

'A' can be placed in any of the 6 odd positions - 6 ways
'I' can be placed in any of the remaining 5 odd positions - 5 ways
'I' can be placed in any of the remaining 4 odd positions - 4 ways

Total ways to arrange vowels = 6*5*4/2 = 60 ways ('I' repeats twice, so we need to divide it by 2).

AND
Remaining eight consonants can be arranged in  \frac{8!}{2!	imes 2! }

Total number of words =  60 	imes \frac{8!}{4}= 15 	imes 8! . Answer: B

Thanks.

Saurabhminocha · Answer

6 odd spaces and 3 vowels- 6C3 and arrange them in 3!/2! ways, since 2 vowels are same (letter i).
remaining 8 letters are arranged in 8!/2!*2! ways, since letters g and t are repeated.

6C3 * 3!/2! * 8!/2!*2! = 15*8! (B)

Fdambro294 · Answer

Out of 11 slots, 6 will be odd (1 , 3 , 5 , 7 , 9 , 11)

Out of the 6 odd slots, we need to find out how many ways we can choose 3 of them to place the vowels A, I, and I in.

(6 c 3)

Then for each combination of 3 slots chosen, we can arrange the 3 vowels (2 of which are identical) in:

3! / 2! = 3 ways

Finally, the remaining 8 letters can be arranged in the remaining 8 spots in 8! Ways

However, since the G and T consonants are repeated, we will have overcounted the number of unique arrangements.

8! / (2! 2!)

Final Answer:

(6 c 3) (3)   =

(20) (3)   =

(5) (3)   =

(15) * (8!)

Posted from my mobile device

rvgmat12 · Answer

11 letters - 3 vowels

6 spots for vowels - {1,3,5,7,9,11}

Arrange the vowels in 6C3*3!/2! = 20*3 = 60 ways

Arrange the rest in 8!/(2!*2!)

Total = 8!/(2!*2!)*60 = 8!*15

Archit3110 · Answer

total characters 11
Vowels = AII ; 3
Consonants = 8 ; GMTNSGHT 
Total odd places 6 and even places 5
for vowel places AII can be arranged in odd places ; 6*5*4 /2 ; 60 ways
for '8' consonants they can be arranged in 8!/ 2!*2! ; 8!/4 
total possible arrangements ; 60*8!/4 ; 15*8! 
option B

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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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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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