Question

14. A company is evaluating 6 investment proposals. If 3 of them have to be selected
simultaneously, the number of different selections are
a. 9
b. 16
c. 20
d. 40​

Answer 1

SOLUTION

TO CHOOSE THE CORRECT OPTION

A company is evaluating 6 investment proposals. If 3 of them have to be selected simultaneously, the number of different selections are

a. 9

b. 16

c. 20

d. 40

EVALUATION

A company is evaluating 6 investment proposals

Now 3 of them have to be selected simultaneously

Hence the number of different selections

$\sf{ = {}^{6}C_3 }$

$\displaystyle \sf{ = \frac{6!}{3! \: 3!} }$

$\displaystyle \sf{ = \frac{6 \times 5 \times 4 \times 3!}{(3 \times 2 \times 1) \times \: 3!} }$

$\displaystyle \sf{ = \frac{6 \times 5 \times 4 }{3 \times 2 \times 1} }$

$= 20$

Hence the correct option is

c. 20

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