Question

Please help! Correct answer gets a medal!!

There are 9 items at the salad bar.


How many ways can Gwen select 3 items from the salad bar?

A. 3

B. 27

C. 84

D. 504

Answer 1

I think you basically asked,\[9 ~~~nCr~~~3\]

Answer 2

what??

Answer 3

would it be like 9! divided by 3! or?

Answer 4

nCr = n!/(r!(n - r)!)

Answer 5

\[\huge\color{red}{ nCr=\frac{9!}{3!(9-3)!} }\]

Answer 6

so its C?

Answer 7

84

Answer 8

\[9-3=6~~~~~~~so,\]\[\color{red}{ \frac{9!}{3! \times 6!} }\]
\[9!=6! \times 7 \times 8 \times 9\]
and 6! cancels. YOU HAVE LEFT.\[\color{red}{ \frac{7 \times 8 \times 9}{1 \times 2 \times 3} }\]

Answer 9

\[7 \times 4 \times 3=84\]

Answer 10

You are correct, and fast!