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 (4(45!)+46!)/150(44!)
𝐒𝐨𝐥𝐮𝐭𝐢𝐨𝐧:
First, let's simplify the numerator:
4(45!) + 46!
Recall that 46! = 46 × 45!
So, the numerator becomes:
4(45!) + 46 × 45!
Factor out 45!:
(4 + 46) × 45! = 50 × 45!
Now, let's look at the denominator:
150(44!)
We need to relate 45! to 44!. Recall that 45! = 45 × 44!
Now, divide the numerator by the denominator:
(50 × 45!) / (150 × 44!)
Substitute 45! = 45 × 44!:
(50 × 45 × 44!) / (150 × 44!)
Cancel out 44! from the numerator and the denominator:
(50 × 45) / 150
Simplify the expression:
(50 × 45) / (3 × 50) (since 150 = 3 × 50)
Cancel out 50 from the numerator and the denominator:
45 / 3 = 15
Therefore, (4(45!) + 46!) / (150(44!)) = 15.