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

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