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

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

   Hint (a):

   Begin with $12$, $(12−1)$ $\ldots$ 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 $_nP_6$?

   Hint (c):

   Remember the meaning of $_nP_6$: choose and arrange $6$ items from a collection of $n$ items.

   Answer (c):

   $n(n − 1)(n − 2)(n − 3)(n − 4)(n − 5)$