permutation combination

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show that 6!^5! is a divisor of (6!)!

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Devil ·2009-08-01 07:25:26

Check in 6!, largest prime factor is 5, so power of 5 in 720! should be 5!, which is true.....Hence proved.

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Hari Shankar ·2009-08-01 09:14:30

The product of any n consecutive numbers is divisible by n!

(6!)! consists of 6! = 5! X 6 numbers i.e. 5! sets of 6 consecutive numbers. Since each of the sets is divisible by 6!, their product is divisible by 6!^5!.

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Basic Integral Calculus Operators Symbols Matrix Cases

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° ∂ ∞ α β γ δ θ λ μ ν ξ π ρ σ φ ω ε ƒ κ τ υ Γ Δ Λ Σ Π Ω

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permutation combination

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