The first four factors of $7!$ are $7, 6, 5, \text { and } 4 \text{ or } 7, \left(7 − 1\right), \left(7 − 2\right), \text{ and }\left(7 − 3\right)$.

1. Show the first four factors of $12!$ in the same way the factors of $7!$ are shown above.

   Hint (a):

   Begin with 12, (12−1) ... and write out four factors.

2. What are the first six factors of $n!$?

   Hint (b):

   Write them in the same way you wrote the factors for part (a).

3. What is _{$_{n}P_{6}$}?

   Hint (c):

   Remember the meaning of _{$_{n}P_{6}$}: choose and arrange $6$ items from a collection of $n$ items.

   Answer (c):

   $n\left(n − 1\right)\left(n − 2\right)\left(n − 3\right)\left(n − 4\right)\left(n − 5\right)$