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# An Architect has 4 design samples to choose as basis for his

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An Architect has 4 design samples to choose as basis for his [#permalink]  30 Jun 2008, 08:15
An Architect has 4 design samples to choose as basis for his new work. He may elect to choose any of these 4 design templates or start a new design sample all together. What are the maximum possible combination for his decision?

OK so I made this question up..the trick is do you count 0 as an option?
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Re: architect [#permalink]  30 Jun 2008, 08:17
Sure. You wrote it in the question: "or start a new design sample"

Edit : I would say the answer to be 2^4 = 16
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Re: architect [#permalink]  30 Jun 2008, 08:24
Oski wrote:
Sure. You wrote it in the question: "or start a new design sample"

Edit : I would say the answer to be 2^4 = 16

can you explain why 2^4 and not 2^5???
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Re: architect [#permalink]  30 Jun 2008, 08:31
fresinha12 wrote:
can you explain why 2^4 and not 2^5???

You have 4 elements from which to choose.

What you want is exactly the number of distinct subsets from a set of n elements (where n=4 in your example). The empty subset being one of them.

Try it for 2 elements if you want. From {1,2} the different subsets are:
{}
{1}
{2}
{1,2}

==> 2^2 = 4 subsets
Current Student
Joined: 28 Dec 2004
Posts: 3391
Location: New York City
Schools: Wharton'11 HBS'12
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Re: architect [#permalink]  30 Jun 2008, 08:36
Oski wrote:
fresinha12 wrote:
can you explain why 2^4 and not 2^5???

You have 4 elements from which to choose.

What you want is exactly the number of distinct subsets from a set of n elements (where n=4 in your example). The empty subset being one of them.

Try it for 2 elements if you want. From {1,2} the different subsets are:
{}
{1}
{2}
{1,2}

==> 2^2 = 4 subsets

OSKI that was great +1 ..i was struggling with 4 or 5...
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Re: architect [#permalink]  30 Jun 2008, 08:38
I don't get the question. How many designs from the 4 available designs can he choose? If he only chooses 1 out 4, then it is just 4. But if he does not want to pick from the 4 available designs and draw up 1 on his own, then that would just be 1 possible combination.

fresinha12 wrote:
An Architect has 4 design samples to choose as basis for his new work. He may elect to choose any of these 4 design templates or start a new design sample all together. What are the maximum possible combination for his decision?

OK so I made this question up..the trick is do you count 0 as an option?
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Re: architect [#permalink]  01 Jul 2008, 01:59
Oski wrote:
fresinha12 wrote:
can you explain why 2^4 and not 2^5???

You have 4 elements from which to choose.

What you want is exactly the number of distinct subsets from a set of n elements (where n=4 in your example). The empty subset being one of them.

Try it for 2 elements if you want. From {1,2} the different subsets are:
{}
{1}
{2}
{1,2}

==> 2^2 = 4 subsets

i didnt get this at all !!
Current Student
Joined: 28 Dec 2004
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Schools: Wharton'11 HBS'12
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Re: architect [#permalink]  01 Jul 2008, 07:43
the question is very similar to a probability question that would go like, the probability it will rain is 50% on any given day...what is the probability it will rain 2 days out of 5 days...

here the total possible number of outcomes is 2^5...either it rains or not..there 5 days..so 2^5...

same concept here..i am asking an architect can pick a plan or not.2 outcome..pick, not pick..

there are 4 such instances..
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Re: architect [#permalink]  01 Jul 2008, 07:56
can anyone explain this to me pls...i am not getting it...
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Re: architect [#permalink]  01 Jul 2008, 12:00

Here is the explanation:
As mentioned in the question he can chose any of the 4 designs or create a new 1:
So,
He can make a design by choosing 0 of the 4 designs in 4C0 ways = 1 (Created a new design)
He can make a design by choosing 1 of the 4 designs in 4C1 ways = 4
He can make a design by choosing 2 of the 4 designs in 4C2 ways = 6
He can make a design by choosing 3 of the 4 designs in 4C3 ways = 4
He can make a design by choosing all 4 of the 4 designs in 4C4 ways = 1

Total number of combinations is sum of the above numbers, i.e., 1 + 4 + 6 + 4 + 1 = 16
Re: architect   [#permalink] 01 Jul 2008, 12:00
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