### Home > CCG > Chapter 10 > Lesson 10.3.4 > Problem10-157

10-157.

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.

Begin with $12$$(12−1)$ $\ldots$ and write out four factors.

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

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

3. What is $_nP_6$?

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

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