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 (8!-6(6!))/(3!+4)
๐๐จ๐ฅ๐ฎ๐ญ๐ข๐จ๐ง:
First, let's evaluate the numerator:
8! - 6(6!)
Recall that 8! = 8 ร 7 ร 6! = 56 ร 6!
So, the numerator becomes:
56 ร 6! - 6 ร 6!
Factor out 6!:
(56 - 6) ร 6! = 50 ร 6!
Now, let's evaluate the denominator:
3! + 4
Recall that 3! = 3 ร 2 ร 1 = 6
So, the denominator becomes:
6 + 4 = 10
Now, divide the numerator by the denominator:
(50 ร 6!) / 10
= 5 ร 6!
To get a numerical value, calculate 6!:
6! = 6 ร 5 ร 4 ร 3 ร 2 ร 1 = 720
So, the final value is:
5 ร 720 = 3600
Therefore, (8! - 6(6!)) / (3! + 4) = 3600.