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
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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$$Total\ possible\ items=10$$
$$The\ bundle\ is\ 6\ out\ of\ 10\ items$$
$$Total\ bundles\ =\ 10C6\ =\ \frac{10!}{6!\left(10-6\right)!}$$
$$\ =\ \frac{10!}{6!\left(4\right)!}$$
$$\ =\ \frac{10\cdot9\cdot8\cdot7\cdot6\cdot5\cdot4\cdot3\cdot2\cdot1}{6\cdot5\cdot4\cdot3\cdot2\cdot1\cdot4\cdot3\cdot2\cdot1}$$
$$\ =\ \frac{10\cdot9\cdot8\cdot7}{4\cdot3\cdot2\cdot1}$$
$$\ =\ \frac{5040}{24}$$
$$Total\ bundles\ =\ 210$$
$$Bundles\ e\lim inated\ from\ considertion\ =\ 49$$
$$Potential\ bundles\ under\ consideration\ =\ 210\ -\ 49$$
$$=\ 161$$
$$Answer\ =\ B$$
$$The\ bundle\ is\ 6\ out\ of\ 10\ items$$
$$Total\ bundles\ =\ 10C6\ =\ \frac{10!}{6!\left(10-6\right)!}$$
$$\ =\ \frac{10!}{6!\left(4\right)!}$$
$$\ =\ \frac{10\cdot9\cdot8\cdot7\cdot6\cdot5\cdot4\cdot3\cdot2\cdot1}{6\cdot5\cdot4\cdot3\cdot2\cdot1\cdot4\cdot3\cdot2\cdot1}$$
$$\ =\ \frac{10\cdot9\cdot8\cdot7}{4\cdot3\cdot2\cdot1}$$
$$\ =\ \frac{5040}{24}$$
$$Total\ bundles\ =\ 210$$
$$Bundles\ e\lim inated\ from\ considertion\ =\ 49$$
$$Potential\ bundles\ under\ consideration\ =\ 210\ -\ 49$$
$$=\ 161$$
$$Answer\ =\ B$$
Total selection would be \(10C6 = 210\) and order won't matter, so no arrangements required.BTGmoderatorDC wrote: ↑Tue Nov 24, 2020 8:26 pmA 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
The question further says, \(49\) bundles eliminated.
So, \(210 - 49 = 161 \Longrightarrow\) B
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Solution:BTGmoderatorDC wrote: ↑Tue Nov 24, 2020 8:26 pmA 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
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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