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

[BTGmoderatorDC]

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

[deloitte247]

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

[swerve]

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

[Scott@TargetTestPrep]

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