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# The letters D, G, I, I , and T can be used to form 5-letter strings as

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BSchool Forum Moderator
Joined: 26 Feb 2016
Posts: 2256
Location: India
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The letters D, G, I, I , and T can be used to form 5-letter strings as [#permalink]

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07 Mar 2018, 11:31
Bunuel wrote:
The letters D, G, I, I , and T can be used to form 5-letter strings as DIGIT or DGIIT. Using these letters, how many 5-letter strings can be formed in which the two occurrences of the letter I are separated by at least one other letter?

A) 12
B) 18
C) 24
D) 36
E) 48

Total possibilities of forming 5 letter words with alphabets D I G I T is 5*4*3*2*1

Here, there are 5 possibilities for the first position, 4 for the second position, 3 for the third position,
2 for the second position, and 1 for the final position

However, since we have 2 I's, we divide the total possibilities by 2

Total possibilities with digits D I G I T are $$\frac{5*4*3*2*1}{2} = 60$$

Possibilities when the two I's are together
Consider the 2 I's as 1 unit. Let's call it X.
For the digits X D G T, Total possibilities are 4*3*2*1 = 24

Possibilities where I's are not together = Total possibilities - possibilities when they come together = 60-24 = 36

Therefore, the total possibilities in which the two occurrences of I aren't together is 36(Option D)
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Re: The letters D, G, I, I , and T can be used to form 5-letter strings as [#permalink]

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09 Mar 2018, 01:26
pushpitkc wrote:
Bunuel wrote:
The letters D, G, I, I , and T can be used to form 5-letter strings as DIGIT or DGIIT. Using these letters, how many 5-letter strings can be formed in which the two occurrences of the letter I are separated by at least one other letter?

A) 12
B) 18
C) 24
D) 36
E) 48

Total possibilities of forming 5 letter words with alphabets D I G I T is 5*4*3*2*1

Here, there are 5 possibilities for the first position, 4 for the second position, 3 for the third position,
2 for the second position, and 1 for the final position

However, since we have 2 I's, we divide the total possibilities by 2

Total possibilities with digits D I G I T are $$\frac{5*4*3*2*1}{2} = 60$$

Possibilities when the two I's are together
Consider the 2 I's as 1 unit. Let's call it X.
For the digits X D G T, Total possibilities are 4*3*2*1 = 24

Possibilities where I's are not together = Total possibilities - possibilities when they come together = 60-24 = 36

Therefore, the total possibilities in which the two occurrences of I aren't together is 36(Option D)

I solved this by this method No case is possible with 2 I together so if we subtract total no. of cases with the cases of 2 I together than that will be our answer
total cases are 5!/2! (total letters/repeated letters)
together case is 4!*2!/2!(two i together counted as 1 then total letter is 4* both 2 can exchange their places/2 repeated no.)
=4!
5*4*3-4*3*2*1
=4*3(5-2)
=12(3)=36
Re: The letters D, G, I, I , and T can be used to form 5-letter strings as   [#permalink] 09 Mar 2018, 01:26

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