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How many three-digit integers can be created from 5 distinc

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How many three-digit integers can be created from 5 distinc [#permalink] New post 24 May 2017, 01:49
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How many three-digit integers can be created from 5 distinct digits?

A) 10

B) 15

C) 20

D) 30

E) 60
[Reveal] Spoiler: OA

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Re: How many three-digit integers can be created from 5 distinc [#permalink] New post 20 Sep 2017, 07:09
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If we were in a case in which the order does not matter, the answer would have been 5C3 = 10. But since in this case the order matter because, for example, 123 is different from 213, we have to multiply 5C3 by the number of ways in which 3 elements can be ordered, i.e. 3! = 6. Thus, we have 10*6 = 60 and answer is E!
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Re: How many three-digit integers can be created from 5 distinc [#permalink] New post 18 Feb 2018, 18:21
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you can also use 5P3 instead 5C3 in order to get the answer faster. 5P3=5X4X3=60
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Re: How many three-digit integers can be created from 5 distinc [#permalink] New post 19 Apr 2018, 16:24
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hugebigmac wrote:
you can also use 5P3 instead 5C3 in order to get the answer faster. 5P3=5X4X3=60

This question seems troublesome for me. What if 0 is included in the 5 distinct given digits?
Assuming that 0 is not included in the 5 given digits, I think that 5*5*5=125 should be the answer instead of 60 since integers with 3 similar digits must also be included.
Please let me know your thought!
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Re: How many three-digit integers can be created from 5 distinc [#permalink] New post 19 Apr 2018, 17:59
halam wrote:
hugebigmac wrote:
you can also use 5P3 instead 5C3 in order to get the answer faster. 5P3=5X4X3=60

This question seems troublesome for me. What if 0 is included in the 5 distinct given digits?
Assuming that 0 is not included in the 5 given digits, I think that 5*5*5=125 should be the answer instead of 60 since integers with 3 similar digits must also be included.
Please let me know your thought!


@Carcass,

Kindly have a re-look at this question! Seems to be a poorly framed one!
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Re: How many three-digit integers can be created from 5 distinc [#permalink] New post 21 Apr 2018, 05:04
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what do you mean ??

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Re: How many three-digit integers can be created from 5 distinc [#permalink] New post 21 Apr 2018, 07:35
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Carcass wrote:
what do you mean ??

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Two things:

All the answers here assume digits cannot be repeated. Why? Does the question mention so?

The question states: "How many three-digit integers can be created from 5 distinct digits?"

If we assume five distinct digits to be {1,2,3,4,5}

Can't I create three digit integer "111" form the above set of numbers?

Per the question, 111 is a three-digit integer that "can be created" from the given set of numbers
Per the question, 112 is another three-digit integer that "can be created" from the given set of numbers.

And so on and so forth...

Maybe the author meant to say "How many 3 digit integers with distinct digits can be created from 5 distinct digits?"

So, if we assume 1,2,3,4,5 to be the 5 digits we get following 60 three digit integers with "distinct digits"

123 124 125 134 135 145 234 235 245 345
132 142 152 143 153 154 243 253 254 354
213 214 215 314 315 415 324 325 425 435
231 241 251 341 351 451 342 352 452 453
312 412 512 413 513 514 423 523 524 534
321 421 521 431 531 541 432 532 542 543

These could be the combinations that the author might have visualized. But to get these, question should have been modified to ensure digits are not repeated!!

But the problem does not end here!!!

What if "0" is a digit out of the 5 distinct digits?? For example: {0,1,2,3,4}

Here I cannot have 012, 013 etc. as three digit integers. So the number of possibilities will reduce further!

Isn't the question ambiguous?
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Re: How many three-digit integers can be created from 5 distinc [#permalink] New post 21 Apr 2018, 08:29
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Yes, you are right.

the problem is one: it comes from a NON-official source. This is a good chance to learn that official material is the only one-stop solution resource in the last stage of your preparation for the exam. The rest is good to practice.

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Re: How many three-digit integers can be created from 5 distinc [#permalink] New post 21 Apr 2018, 08:33
Thanks to @halam for pointing this out.

@Carcass, maybe this question should be marked as "Poor question" so that other students don't get confused!
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Re: How many three-digit integers can be created from 5 distinc [#permalink] New post 21 Apr 2018, 08:50
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Well, after all, it is from Princeton. A really well-established prep company.

If we do start to label which one is poor or bad or else we will end up to study with only the Official material.

Instead, think this way: what do we learn from a question like this, with the help of the guys here on the board ?? to spot where is a possible pitfall.

This is useful to improve our skills and see a question "behind the lines". Therefore, there is something positive from which we can have benefit.

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Re: How many three-digit integers can be created from 5 distinc [#permalink] New post 29 Sep 2018, 11:53
It's permutation math. 5P3 = 60. So, the answer is E
Re: How many three-digit integers can be created from 5 distinc   [#permalink] 29 Sep 2018, 11:53
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