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MERCURYZ.EXE
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CARDS.EKA
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1992-03-24
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681b
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; This example demonstrates how to use Mercury's built-in
; FACT function (FACT(x) = x factorial). The problem is:
; In a bridge game, the declarer controls 7 trump cards.
; We must determine the probability that the remaining
; 6 trump cards are evenly distributed (3 and 3) among
; the opposing two players. We calculate both the
; approximate and the exact probability in this example.
; the binomial coefficient formula
; ways of choosing k of n items
C(n,k) := BINOM(n,k) ; = FACT(n) / (FACT(k) FACT(n-k))
; approximate probability of 3-3 split
ProbApprox = C(6,3) / 2^6
; exact probability of 3-3 split
ProbExact = C(6,3) * C(20,10) / C(26,13)