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# Perms + Combination 3

Author Message
Intern
Joined: 06 May 2012
Posts: 5

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20 May 2012, 12:22
the last question for today!!

How many different codes can be formed using the five letters of the word DIGIT, if the two Is cannot be next to each other?
a. 120
b. 60
c. 56
d. 46
e 36

Kindly help me to get the answer of this question. Thks again!

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VP
Joined: 24 Jul 2011
Posts: 1343

Kudos [?]: 637 [0], given: 20

GMAT 1: 780 Q51 V48
GRE 1: 1540 Q800 V740
Re: Perms + Combination 3 [#permalink]

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20 May 2012, 18:07
The letters of the word DIGIT excluding the two Is are D,G,T

They can be arranged in the following way:
x - Letter 1 - x - Letter 2 - x - Letter 3 - x

The three digits D,G,T can occupy the positions marked by Letter 1, Letter 2, and Letter 3 in 3! ways = 6 ways
The Two Is can be placed in any of the positions marked by x = 4C2 ways = 6 ways

Total number of ways = 6 x 6 = 36

Option (E)
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Kudos [?]: 637 [0], given: 20

Re: Perms + Combination 3   [#permalink] 20 May 2012, 18:07
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