Answer:
Either 10,800 (the way the problem is written)
or 1/48 (perhaps what problem was meant to be)
See below.
Explanation:
5!7!/8!6!
The real meaning of the problem as given is (where only 8! is in the denominator):
5! × 7!/8! × 6! =
= 5 × 4 × 3 × 2 × 1 × 7 × 6 × 5 × 4 × 3 × 2 × 1/(8 × 7 × 6 × 5 × 4 × 3 × 2 × 1) × 6 × 5 × 4 × 3 × 2 × 1
= 5 × 4 × 3 × 2 × 1 × 7 / (8 × 7) × 6 × 5 × 4 × 3 × 2 × 1
= 5 × 3 × 6 × 5 × 4 × 3 × 2
= 10,800
Perhaps you meant this:
5!7!/(8!6!) =
= (5 × 4 × 3 × 2 × 1 × 7 × 6 × 5 × 4 × 3 × 2 × 1)/(8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 × 6 × 5 × 4 × 3 × 2 × 1)
= 1/(8 × 6)
= 1/48