Question

How many ways can a committee of 6 be selected from a club with 10 ​members

Answer 1

210

Explanation:

The general formula for picking k items from a total of n is

`_(n)C_(k) = (n! )/((n-k)!k! )`

Thus, if we want to select a committee of six people from a club with 10 members, the number of combinations is

`_(10)C_(6) = (10! )/((10-6)!6! )`

`= (10! )/(4!6! )`

`= (10*9*8*7)/(4*3*2*1 )`

`= (5040 )/(24 )`

= 210

The committee can be selected in 210 separate ways.