At a certain laboratory, chemical substance are identified by an unordered combination of three different...

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BTGmoderatorLU: Moderator; Posts: 2650; Joined: Sun Oct 15, 2017 1:50 pmFollowed by: 6 members

by BTGmoderatorLU » Sat Dec 19, 2020 3:27 am

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Source: Veritas Prep

At a certain laboratory, chemical substance are identified by an unordered combination of three different colors. If no chemical may be assigned the same three colors as any other, what is the maximum number of substances that can be identified using seven colors?

A. 21
B. 35
C. 105
D. 135
E. 210

The OA is B

Source: Beat The GMAT — Problem Solving | Sat Dec 19, 2020 3:27 am

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

Re: At a certain laboratory, chemical substance are identified by an unordered combination of three different...

by deloitte247 » Mon Dec 28, 2020 1:32 am

In permutation and combination, an unordered combination is of the form nCr, which has the formula =>
$$\frac{n!}{r!\cdot\left(n-r\right)!}$$
Total colors available = 7
And we need to choose 3 colors. So, we find 7C3
$$7C_3=\frac{7!}{3!\cdot\left(7-3\right)!}$$
$$=\frac{7!}{3!4!}$$
$$=\frac{7\cdot6\cdot5\cdot4!}{3\cdot2\cdot1\cdot4!}=\frac{7\cdot6\cdot5}{3\cdot2}=35$$
Answer = option B

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Re: At a certain laboratory, chemical substance are identified by an unordered combination of three different...

by Scott@TargetTestPrep » Sat Jan 02, 2021 2:17 pm

BTGmoderatorLU wrote: ↑
Sat Dec 19, 2020 3:27 am
Source: Veritas Prep

At a certain laboratory, chemical substance are identified by an unordered combination of three different colors. If no chemical may be assigned the same three colors as any other, what is the maximum number of substances that can be identified using seven colors?

A. 21
B. 35
C. 105
D. 135
E. 210

The OA is B

Solution:

The number of ways of choosing 3 colors out of 7 (where order doesn’t matter) is 7C3 = 7! / (3! x 4!) = (7 x 6 x 5) / (3 x 2) = 7 x 5 = 35.

Answer: B

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