Learn about factorials and how to evaluate expressions that contain them. This video explains the concept of factorials and provides step-by-step solutions to several evaluation problems. Perfect for students learning combinatorics or algebra!
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𝐐𝐮𝐞𝐬𝐭𝐢𝐨𝐧: Evaluate (16!-40(14!))/50(13!)
𝐒𝐨𝐥𝐮𝐭𝐢𝐨𝐧:
First, let's simplify the numerator:
16! - 40(14!)
Recall that 16! = 16 × 15 × 14!
So, the numerator becomes:
(16 × 15 × 14!) - 40 × 14!
Factor out 14!:
(16 × 15 - 40) × 14!
Calculate 16 × 15:
16 × 15 = 240
So, the numerator is:
(240 - 40) × 14! = 200 × 14!
Now, let's look at the denominator:
50(13!)
We need to relate 14! to 13!. Recall that 14! = 14 × 13!
Now, divide the numerator by the denominator:
(200 × 14!) / (50 × 13!)
Substitute 14! = 14 × 13!:
(200 × 14 × 13!) / (50 × 13!)
Cancel out 13! from the numerator and the denominator:
(200 × 14) / 50
Simplify the expression:
(200 × 14) / 50 = (4 × 14) / 1
Calculate 4 × 14:
4 × 14 = 56
Therefore, (16! - 40(14!)) / (50(13!)) = 56.