Question

How many ways can you pick 4 students from 10 students (6 men, 4 women)?

Answer 1

Consider this option:
for 4 person from 10: C⁴₁₀.
It means C₁₀⁴ =  $\frac{10!}{4!6!}= \frac{7*8*9}{4!}= \frac{7*8*9}{24}=21.$

Answer: 21 ways.

Answer 2

Answer:

There are 210 ways in which you can pick 4 students from 10 students (6 men, 4 women).

Step-by-step explanation:

We use the combination formula because the order does not matter.

For example, John, Laura,... is the same way as Laura, then John, then ...

Combinations formula

$C_{n,x}$ is the number of different combinatios of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

In this problem, we have that:

Combinations of 4 students from a set of 10. So

$C_{10,4} = \frac{10!}{4!(10-4)!} = 210$

There are 210 ways in which you can pick 4 students from 10 students (6 men, 4 women).