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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๐๐ฎ๐๐ฌ๐ญ๐ข๐จ๐ง: Evaluate (16!-40(14!))/50(13!)
๐๐จ๐ฅ๐ฎ๐ญ๐ข๐จ๐ง:
First, let's simplify the numerator:
16! - 40(14!)
Recall that 16! = 16 ร 15 ร 14!
So, the numerator becomes:
(16 ร 15 ร 14!) - 40 ร 14!
Factor out 14!:
(16 ร 15 - 40) ร 14!
Calculate 16 ร 15:
16 ร 15 = 240
So, the numerator is:
(240 - 40) ร 14! = 200 ร 14!
Now, let's look at the denominator:
50(13!)
We need to relate 14! to 13!. Recall that 14! = 14 ร 13!
Now, divide the numerator by the denominator:
(200 ร 14!) / (50 ร 13!)
Substitute 14! = 14 ร 13!:
(200 ร 14 ร 13!) / (50 ร 13!)
Cancel out 13! from the numerator and the denominator:
(200 ร 14) / 50
Simplify the expression:
(200 ร 14) / 50 = (4 ร 14) / 1
Calculate 4 ร 14:
4 ร 14 = 56
Therefore, (16! - 40(14!)) / (50(13!)) = 56.