A cosmetics company would like to market a six-item gift basket bundle from a set of ten possible items. If 49 of the

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BTGmoderatorDC: Moderator; Posts: 7187; Joined: Thu Sep 07, 2017 4:43 pmFollowed by: 23 members

by BTGmoderatorDC » Tue Nov 24, 2020 8:26 pm

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A cosmetics company would like to market a six-item gift basket bundle from a set of ten possible items. If 49 of the potential bundles have already been eliminated from consideration, how many potential bundles are still being considered?

A. 147
B. 161
C. 175
D. 182
E. 210

OA B

Source: Veritas Prep

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Source: Beat The GMAT — Problem Solving | Tue Nov 24, 2020 8:26 pm

deloitte247: Legendary Member; Posts: 2214; Joined: Fri Mar 02, 2018 2:22 pmFollowed by: 5 members

Re: A cosmetics company would like to market a six-item gift basket bundle from a set of ten possible items. If 49 of th

by deloitte247 » Fri Nov 27, 2020 8:13 am

$$Total\ possible\ items=10$$
$$The\ bundle\ is\ 6\ out\ of\ 10\ items$$
$$Total\ bundles\ =\ 10C6\ =\ \frac{10!}{6!\left(10-6\right)!}$$
$$\ =\ \frac{10!}{6!\left(4\right)!}$$
$$\ =\ \frac{10\cdot9\cdot8\cdot7\cdot6\cdot5\cdot4\cdot3\cdot2\cdot1}{6\cdot5\cdot4\cdot3\cdot2\cdot1\cdot4\cdot3\cdot2\cdot1}$$
$$\ =\ \frac{10\cdot9\cdot8\cdot7}{4\cdot3\cdot2\cdot1}$$
$$\ =\ \frac{5040}{24}$$
$$Total\ bundles\ =\ 210$$
$$Bundles\ e\lim inated\ from\ considertion\ =\ 49$$
$$Potential\ bundles\ under\ consideration\ =\ 210\ -\ 49$$
$$=\ 161$$
$$Answer\ =\ B$$

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swerve: Legendary Member; Posts: 2545; Joined: Sun Oct 29, 2017 2:04 pmFollowed by: 6 members

Re: A cosmetics company would like to market a six-item gift basket bundle from a set of ten possible items. If 49 of th

by swerve » Fri Nov 27, 2020 3:59 pm

BTGmoderatorDC wrote: ↑
Tue Nov 24, 2020 8:26 pm
A cosmetics company would like to market a six-item gift basket bundle from a set of ten possible items. If 49 of the potential bundles have already been eliminated from consideration, how many potential bundles are still being considered?

A. 147
B. 161
C. 175
D. 182
E. 210

OA B

Source: Veritas Prep

Total selection would be $10C6 = 210$ and order won't matter, so no arrangements required.

The question further says, $49$ bundles eliminated.

So, $210 - 49 = 161 \Longrightarrow$ B

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8155; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

Re: A cosmetics company would like to market a six-item gift basket bundle from a set of ten possible items. If 49 of th

by Scott@TargetTestPrep » Mon Nov 30, 2020 9:17 am

BTGmoderatorDC wrote: ↑
Tue Nov 24, 2020 8:26 pm
A cosmetics company would like to market a six-item gift basket bundle from a set of ten possible items. If 49 of the potential bundles have already been eliminated from consideration, how many potential bundles are still being considered?

A. 147
B. 161
C. 175
D. 182
E. 210

OA B

Solution:

We first can determine how many 6-item bundles can be created from 10 items.

10C6 = 10!/(6!4!) = (10 x 9 x 8 x 7)/(4 x 3 x 2 x 1) = 5 x 3 x 2 x 7 = 210

Since 49 bundles have been removed from consideration, 210 - 49 = 161 bundles are still being considered.

Answer: B

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Founder and CEO
[email protected]

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