Explanation: The quantity "5!" is read as "five factorial" and is the product of 5 * 4 * 3 * 2 * 1 which is 120. The values of the first 10 factorials are 1! = 1, 2! = 2 * 1 = 2, 3! = 3 * 2 * 1 = 6, 4! = 4 * 3 * 2 * 1 = 24, 5! = 5 * 4 * 3 * 2 * 1 = 120, 6! = 6 * 5 * 4 * 3 * 2 * 1 = 720, 7! = 7 * 6 * 5 * 4 * 3 * 2 * 1 = 5,040, 8! = 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 = 40,320 9! = 362,880 and 10! = 3,628,800.

Examples: 5!/3! = (5*4*3*2*1)/(3*2*1) Notice the 3*2*1 cancel, so the answer is 5*4 which is 20

3!/5! = (3*2*1)/(5*4*3*2*1) Notice the 3*2*1 cancel, so the answer is 1/(5*4) which is 1/20

48/4! = 48/(4*3*2*1) = 48/24 = 2

Directions: Write down the values of the ten factorials so you may use them as you find the value of these numerical factorial expressions. Strive to understand the simplest way to accomplish the problems, then strive to increase your speed. Good luck and enjoy the challenge!