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

[BTGmoderatorLU]

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

[deloitte247]

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

[Scott@TargetTestPrep]

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