Question

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

Answer 1

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