Question

lorelei evaluates the expression \\(\frac{12!}{(12 - 10)!10!}\\) to determine how many different groups of ten she can make out of twelve items.
lorelei’s work

1. subtract within parentheses and simplify: \\(\frac{6!}{(2)!5!}\\)
2. expand: \\(\frac{6\cdot5\cdot4\cdot3\cdot2\cdot1}{2\cdot1\cdot5\cdot4\cdot3\cdot2\cdot1}\\)
3. divide out common factors: \\(\frac{6}{2\cdot1}\\)
4. because 6 divided by \\(2 \cdot 1\\) is 3, there are 3 ways to choose the groups.

which statements describe lorelei’s solution? choose two correct answers.

• 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!\\).
• her work is correct.
• her answer is correct.

Explanation:

Answer:

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 \(5!\).