Final answer:
To evaluate the expression 5!7!/8!6!, simplify the factorials and then perform the division. The simplified result is 1/48.
Step-by-step explanation:
To evaluate the expression 5!7!/8!6!, we need to simplify the factorials and then perform the division. Let's start by simplifying the factorials:
5! means 5 factorial, which is equal to 5 x 4 x 3 x 2 x 1.
7! means 7 factorial, which is equal to 7 x 6 x 5 x 4 x 3 x 2 x 1.
8! means 8 factorial, which is equal to 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1.
6! means 6 factorial, which is equal to 6 x 5 x 4 x 3 x 2 x 1.
Now, let's simplify the expression:
5!7!/8!6! = (5 x 4 x 3 x 2 x 1 x 7 x 6 x 5 x 4 x 3 x 2 x 1) / (8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 x 6 x 5 x 4 x 3 x 2 x 1)
Simplifying further, we can cancel out the common factors:
5!7!/8!6! = (1) / (8 x 6) = 1/48