Question

Three out of seven students in the cafeteria line are chosen to answer survey questions. How many different combinations of three students are possible?

Answer 1

35 possible combinations would be there.

Explanation:

We have total of seven students we have to choose three out of those seven

`^(n)C_r=(n!)/(r!\cdot (n-r)!)`

n is the total possibilities n =7 in the given case

And r is the chosen ones

Hence, r=3 in the given case.

Substituting the values of n and r in the formula we get

`^(7)C_3`

`(7!)/(3!(7-3)!)`

`(7!)/(3!\cdot 4!)`

Using n!=n(n-1)----1

`(7\cdot 6\cdot 5\cdot 4!)/(3\cdot 2\cdot 1\cdot 4!)`

Cancel the common factor we get

`35` possible combinations would be there.