why is 0 != 1 (prove)
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0 factorial is used mainly in permutation and combination. In that field of maths, it denotes the number of ways in which 0 things can be arranged in 0 places, which equals one (the only way is not arranging anything, that's the one way). So, 0 factorial is equal to 1.
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Step-by-step explanation:
To Prove:- 0! =1. Known: y! = y x (y-1)! So, 1! = 1 x (1-1)! 1! = 0! or 0! = 1! -(a) Proof: As We know, n! = n x n-1 x n-2 x n-3 x n-4 x .......... 2 x 1 So, 4! = (3+1)! = 4 x 3! = 4 x 3 x 2 x 1 3! = (2+1)! = 3 x 2! = 3 x 2 x 1 2! = (1+1)! = 2 x 1! = 2 x 1 1! = (0+1)! = 1 x 0! = 1 -(b) Hence, from (a) and (b) We get, 0! = 1
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