simplify the following factorials.
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Answer:
1. 720
2. 336
3. 384
4. 1/4
Step-by-step explanation:
1. 6! = 6x5x4x3x2x1 = 720
2. 8!/5! = (8x7x6x5x4x3x2x1) / (5x4x3x2x1)
Cancel the same number, it gives us:
= 8x6x7 = 336
3. [9! / (9-3)!] - 5! = (9! / 6!) - 5!
= [(9x8x7x6x5x4x3x2x1) / (6x5x4x3x2x1)] - 5!
Cancel the same number:
= (9x8x7) - (5x4x3x2x1)
= 504 - 120
= 384
4. [(10-4)! / 5!] (1/4!)
= (6!/5!) (1/4!)
= [(6x5x4x3x2x1) / (5x4x3x2x1)] (1/4!)
Same process in #3 (cancel), we get:
= (6) (1/(4x3x2x1))
= 6 (1/24)
= 1/4