In how many ways can 3-digit numbers be formed selecting 3 digits from 1, 1, 2, 3, 4?
1. 5P3/(2!)
2. 4P3
3. 4^3
4. 4P3+3C1*(3!/2!)
5. 60 × 3!
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Combinatorics
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ankitns
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The answer should be [spoiler]A -> 5P3 / (2!)[/spoiler]
We select 3 numbers from 5 possible selections. But since 1 is repeated twice, we divide it by 2!.
Hope it helps.
We select 3 numbers from 5 possible selections. But since 1 is repeated twice, we divide it by 2!.
Hope it helps.
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DanaJ
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You have 5 objects (1, 1, 2, 3, 4) from which you need to choose 3. The order matters, so for this you'll have the formula 5P3. However, since 1 appears 2 times, you'll need to reduce the whole thing by 2!. This is why I am getting A.
I don't think that's right since it's not a pure combination. 112 is still a distinct number from 121, though if you are using the combinations method they will be treated as identical. I believe the OA is (D), I'm just not sure how they got it.
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Ian Stewart
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If you use three different digits, you'd have 4 choices for the hundreds digit, 3 for the tens, and 2 for the units, so 4*3*2 choices in total. If you use two 1's and a different digit (2, 3 or 4), you have three choices for which other digit to use, and three choices for where to put it - the hundreds, tens or units place - so 3*3 numbers you can make with two 1's and something else. So you have 4*3*2 + 3*3 = 24 + 9 = 33 different numbers in total.
You will *never* see the number 33 written as "4P3+3C1*(3!/2!)" in a GMAT question - it's not only an absurd way to write a number as small as 33, but notation like nCr or nPr is not something GMAT test takers are required to know about for the test (in mathematics, there are about a dozen different notations that are used for those quantities - notation like nCr is not standard in mathematics, and many people will have studied a different notation, which is perfectly fine). So I'm curious about the source of the question; the answer choices are not GMAT-like.
You will *never* see the number 33 written as "4P3+3C1*(3!/2!)" in a GMAT question - it's not only an absurd way to write a number as small as 33, but notation like nCr or nPr is not something GMAT test takers are required to know about for the test (in mathematics, there are about a dozen different notations that are used for those quantities - notation like nCr is not standard in mathematics, and many people will have studied a different notation, which is perfectly fine). So I'm curious about the source of the question; the answer choices are not GMAT-like.
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Ahhh... thank you!
I'm not sure what the source of the question is but I'll ask. It was posted on a DS subforum of gmatclub... I take my GMAT in a couple of days and was sort of shocked since I've never seen this type of combinatorics questions before. Thanks for responding!
I'm not sure what the source of the question is but I'll ask. It was posted on a DS subforum of gmatclub... I take my GMAT in a couple of days and was sort of shocked since I've never seen this type of combinatorics questions before. Thanks for responding!
