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# Permutations and Combinations

Author Message
Intern
Joined: 31 Aug 2017
Posts: 3

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23 Nov 2017, 02:04
1
Hi there,

Got a question off the android app: "POCKET GMAT MATH"
I don't agree with the answer they give and would be interested in what people think:

How many different four letter words, with or without meaning, can be formed using the letters of the word GOUVERNMENT such that the first letter is V and the last is N?

I think it should be 57 (7*1+7*6+1*1+1*7)

Interested in what people think

Many thanks

Nicholas
Math Expert
Joined: 02 Aug 2009
Posts: 6202

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23 Nov 2017, 07:44
churchntj wrote:
Hi there,

Got a question off the android app: "POCKET GMAT MATH"
I don't agree with the answer they give and would be interested in what people think:

How many different four letter words, with or without meaning, can be formed using the letters of the word GOUVERNMENT such that the first letter is V and the last is N?

I think it should be 57 (7*1+7*6+1*1+1*7)

Interested in what people think

Many thanks

Nicholas

there are 11 letters..
V and N are already used up, so we have to fill 2 places with 9 available...
but these 9 has 2 Es, so in actual, we have 9-1 = 8 different digits..

choose 2 out of 8 = 8C2 but these 2 can be arranged in 2! ways..
so ways = 8C2*2 = 28*2=56

there is also one way when both letters are E, so 1 more

total 56+1=57

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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Re: Permutations and Combinations   [#permalink] 23 Nov 2017, 07:44
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