Let T(n, r) be the number of ways to put n different balls into r different bins with no bin empty. We have initial conditions T(0,0) = 1, T(n,0) = 0 for n > 1, T(n, 1n) = n!. (1) Arguing similarly to our proof of Pascal's Identity, show that T(n, r) = rT(n – 1,r – 1) +rT(n – 1,r) for 0

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