Evaluate. 10! over 6!(12-8)!

Question

asked Aug 21, 2023 114k views

1 Answer

Jens Lincke · Answer 1 · 2023-08-26T20:15:01+0000

Answer: 210

Explanation:

! means, for example, 6! = 6 * 5* 4 * 3 * 2 * 1

Given:

$\displaystyle (10!)/(6!(12-8)!)$

Subtract:

$\displaystyle (10!)/(6!(4)!)$

Distribute:

$\displaystyle (10!)/(6!*4!)$

Expand:

$\displaystyle (10 * 9 * 8 * 7 * 6 * 5* 4 * 3 * 2 * 1)/((6 * 5* 4 * 3 * 2 * 1)*(4 * 3 * 2 * 1))$

Cancel out (6*5*4*3*2*1) in both the top and bottom as they equal 1:

$\displaystyle (10 * 9 * 8 * 7 )/(4 * 3 * 2 * 1)$

Multiply:

$\displaystyle (5,040 )/(24)$

Divide:

210