DISCRETE MATHEMATICS Prove that for every integer n where n is greater than or equal to 3, P(n+1, 3) - P(n, 3) = 3P(n, 2). For full credit you must use the factorial definition of a permutation. You...

DISCRETE MATHEMATICS


Prove that for every integer n where n is greater than or equal to 3, P(n+1, 3) - P(n, 3) = 3P(n, 2). For full credit you must use the factorial definition of a permutation. You must give your proof line-by-line, with each line a statement with its justification. You must show explicit, formal start and termination statements for the overall proof. In English it would be: For all integers n greater than or equal to 3, the 3-permutation of n+1 elements minus the 3-permutation of n elements is equal to three times the 2-permutation of n elements.