Question

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

Answer 1

Answer:

210

Step-by-step explanation:

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

$_{n}C_{k} = \frac{n! }{(n-k)!k! }$

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

$_{10}C_{6} = \frac{10! }{(10-6)!6! }$

$= \frac{10! }{4!6! }$

$= \frac{10\times9\times8\times7}{4\times3\times2\times1 }$

$= \frac{5040 }{24 }$

= 210

The committee can be selected in 210 separate ways.