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# A newly-wed couple is using a website to design an eBook Wedding Album

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Math Expert
Joined: 02 Sep 2009
Posts: 59572
A newly-wed couple is using a website to design an eBook Wedding Album  [#permalink]

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04 Mar 2015, 04:15
2
3
00:00

Difficulty:

15% (low)

Question Stats:

80% (01:41) correct 20% (02:10) wrong based on 76 sessions

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A newly-wed couple is using a website to design an eBook Wedding Album to distribute to their friends and families. The template they have chosen has places for 3 large photos and 19 smaller photos. The couple has 6 large photos they could use for those three slots, and 21 smaller photos they could use for those 19 slots. Given these choices, how many different possible albums could they create?

A. 3,150
B. 4,200
C. 5,040
D. 20,520
E. 84,000

Kudos for a correct solution.
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Re: A newly-wed couple is using a website to design an eBook Wedding Album  [#permalink]

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04 Mar 2015, 18:50
Bunuel wrote:
A newly-wed couple is using a website to design an eBook Wedding Album to distribute to their friends and families. The template they have chosen has places for 3 large photos and 19 smaller photos. The couple has 6 large photos they could use for those three slots, and 21 smaller photos they could use for those 19 slots. Given these choices, how many different possible albums could they create?

A. 3,150
B. 4,200
C. 5,040
D. 20,520
E. 84,000

Kudos for a correct solution.

For the larger photo they have 6C3 options, which is 20 and for the smaller photo they have 21C19 options, which is 210. 210*20=4200.
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Re: A newly-wed couple is using a website to design an eBook Wedding Album  [#permalink]

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07 Mar 2015, 09:50
1
A similar solution:

For the big album they have to choose 3 out of their 6 photos, and leave out 3:

6! / 3!3! = 20

For the small album they have to choose 19 out of their 21 photos and leave out 2:

21! / 19!2! = 210

All combinations together: 210*20 = 4200, ANS B
Math Expert
Joined: 02 Aug 2009
Posts: 8284
Re: A newly-wed couple is using a website to design an eBook Wedding Album  [#permalink]

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07 Mar 2015, 09:55
Bunuel wrote:
A newly-wed couple is using a website to design an eBook Wedding Album to distribute to their friends and families. The template they have chosen has places for 3 large photos and 19 smaller photos. The couple has 6 large photos they could use for those three slots, and 21 smaller photos they could use for those 19 slots. Given these choices, how many different possible albums could they create?

A. 3,150
B. 4,200
C. 5,040
D. 20,520
E. 84,000

Kudos for a correct solution.

total ways to choose 3 out of 6=6c3=20..
total ways to choose 19 out of 21=21c19=21*20/2=210..
so total ways=20*210=4200 ans B...
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Posts: 59572
Re: A newly-wed couple is using a website to design an eBook Wedding Album  [#permalink]

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08 Mar 2015, 15:25
Bunuel wrote:
A newly-wed couple is using a website to design an eBook Wedding Album to distribute to their friends and families. The template they have chosen has places for 3 large photos and 19 smaller photos. The couple has 6 large photos they could use for those three slots, and 21 smaller photos they could use for those 19 slots. Given these choices, how many different possible albums could they create?

A. 3,150
B. 4,200
C. 5,040
D. 20,520
E. 84,000

Kudos for a correct solution.

MAGOOSH OFFICIAL SOLUTION:

For the large photos, we need 6C3, which we calculated in the article:
6C3 = 20

For the smaller photos, we need 21C19, which by symmetry must equal 21C2, and we have a formula for that. In fact, in the article above, we already calculated that 21C2 = 210.

Now, by the FCP, we just multiply these: total number of possible albums = 20*210 = 4200.

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Re: A newly-wed couple is using a website to design an eBook Wedding Album  [#permalink]

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30 Nov 2019, 12:40
Hi All,

We're told that a newly-wed couple is using a website to design an eBook Wedding Album to distribute to their friends and families. The template they have chosen has places for 3 large photos and 19 smaller photos. The couple has 6 large photos they could use for those three slots, and 21 smaller photos they could use for those 19 slots. We're asked for the number of different possible albums could they create. While the prompt does not explicitly state it, we are meant to assume that placing the same photos in a different order does NOT count as a "new" album, meaning that this is a Combination Formula question.

With the 6 large photos and 3 slots, there are 6c3 = 6!/3!3! = (6)(5)(4)/(3)(2)(1) = 20 possible groups of large photos

With the 21 small photos and 19 slots, there are 21c19 = 21!/19!2! = (21)(20)/(2)(1) = 210 possible groups of small photos

(20)(210) = 4200 possible albums

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Re: A newly-wed couple is using a website to design an eBook Wedding Album   [#permalink] 30 Nov 2019, 12:40
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