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

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VJesus12: Legendary Member; Posts: 2276; Joined: Sat Oct 14, 2017 6:10 am; Followed by:3 members

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

by VJesus12 » Sat Nov 30, 2019 7:20 am

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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

[spoiler]OA=B[/spoiler]

Source: Magoosh

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Source: Beat The GMAT — Problem Solving | Sat Nov 30, 2019 7:20 am

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by [email protected] » Sat Nov 30, 2019 10:47 am

Hi VJesus12,

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

Final Answer: B

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by Scott@TargetTestPrep » Sun Dec 08, 2019 7:16 pm

VJesus12 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

[spoiler]OA=B[/spoiler]

Source: Magoosh

The number of different albums they could create is:

6C3 x 21C19 = 6C3 x 21C2 = (6 x 5 x 4)/(3 x 2) x (21 x 20)/2 = 20 x 210 = 4,200

Answer: B

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