Question

Lorelei evaluates the expression StartFraction 12 factorial Over (12 minus 10) factorial 10 factorial EndFraction to determine how many different groups of ten she can make out of twelve items. Her solution:

Subtract within parentheses and simplify: StartFraction 6 factorial Over (2) factorial 5 factorial EndFraction
Expand: StartFraction 6 times 5 times 4 times 3 times 2 times 1 Over 2 times 1 times 5 times 4 times 3 times 2 times 1 EndFraction
Divide out common factors: StartFraction 6 Over 2 times 1 EndFraction
Because 6 divided by 2∙1 is 3, there are 3 ways to choose the groups.
Which statements describe Lorelei’s solution? Check all that apply.

Her work is correct.
Her answer is correct.
In step 1, the subtraction cannot be completed before the factorial of each number is calculated.
In step 1, 12! divided by 10! is not equivalent to 6! divided by 5!.
In step 3, the dividing out of common factors was performed incorrectly.
There are sixty-six ways to choose ten items from twelve.

Answer 1

D and F

Explanation:

E2020

Answer 2

D. In step 1, 12! divided by 10! is not equivalent to 6! divided by 5!.

F. There are sixty-six ways to choose ten items from twelve.

Explanation:

Edge 2021