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# Given letters ABCCD how many different ways can a group of

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CEO
Joined: 15 Aug 2003
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Given letters ABCCD how many different ways can a group of [#permalink]  18 Sep 2003, 11:53
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Given letters ABCCD how many different ways can a
group of 3 can be formed with these letters.
Intern
Joined: 17 Sep 2003
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Location: GMAT Maze, Chaos.
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Re: PS : Counting Methods # 7 ..letters [#permalink]  18 Sep 2003, 15:16
praetorian123 wrote:
Given letters ABCCD how many different ways can a
group of 3 can be formed with these letters.

Treating the two Cs as 1, we have 4 letters.

The first letter in the group can be chosen in 4 ways, the second letter in 3 ways and the third letter in 2 ways.

So the total number of ways is 4 x 3 x 2 = 24.

Please correct me if I m wrong, my test is on saturday
CEO
Joined: 15 Aug 2003
Posts: 3467
Followers: 61

Kudos [?]: 704 [0], given: 781

Re: PS : Counting Methods # 7 ..letters [#permalink]  18 Sep 2003, 22:29
vasurajiv wrote:
praetorian123 wrote:
Given letters ABCCD how many different ways can a group of 3 can be formed with these letters.

Treating the two Cs as 1, we have 4 letters.

The first letter in the group can be chosen in 4 ways, the second letter in 3 ways and the third letter in 2 ways.

So the total number of ways is 4 x 3 x 2 = 24.

Please correct me if I m wrong, my test is on saturday

This is not permutations. ABC is the same as CBA

try again
Intern
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7. There are 4 different letters A, b,c(2times) and d.

3 letters can be selected in 2 different ways -

first, when all 3 are different - 4c3=4
second, when 2 of the 3 selected are same = 2c2*3c1 = 3

Total groups = 7.
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