Question

Seven students applied for a position on the four-member student review board. In how many ways could four students have been selected for the board? please show me the steps.

Answer 1

\[\dbinom{7}{4}\]
\[\frac{7\times 6\times 5}{3\times 2\times 1}\] cancel first, multiply second

Answer 2

is it 35

Answer 3

you may notice that i chose to compute
\[\dbinom{7}{3}\] which is the same thing because choosing 4 to serve is the same as choosing 3 to exclude

Answer 4

yes, 35

Answer 5

Thank you so much !

Answer 6

yw

Answer 7

I have a question. why we have to exclude 4 in the denominator.Why can't be 7*6*5/4*3*2*1