Answer: 210
Step-by-step explanation:
! means, for example, 6! = 6 * 5* 4 * 3 * 2 * 1
Given:
[tex]\displaystyle \frac{10!}{6!(12-8)!}[/tex]
Subtract:
[tex]\displaystyle \frac{10!}{6!(4)!}[/tex]
Distribute:
[tex]\displaystyle \frac{10!}{6!*4!}[/tex]
Expand:
[tex]\displaystyle \frac{10 * 9 * 8 * 7 * 6 * 5* 4 * 3 * 2 * 1}{(6 * 5* 4 * 3 * 2 * 1)*(4 * 3 * 2 * 1)}[/tex]
Cancel out (6*5*4*3*2*1) in both the top and bottom as they equal 1:
[tex]\displaystyle \frac{10 * 9 * 8 * 7 }{4 * 3 * 2 * 1}[/tex]
Multiply:
[tex]\displaystyle \frac{5,040 }{24}[/tex]
Divide:
210
