The binomial distribution applies only to cases involving two types of outcomes, whereas the multinomial distribution involves more than two categories. Suppose we have three types of mutually exclusive outcomes denoted by A, B, and C. Let P(A) = p₁, P(B) = p₂, and P(C) = p₃. In n independent trials, the probability of x₁ outcomes of type A, x₂ outcomes of type B, and x₃ outcomes of type C is given by

A genetics experiment involves 6 mutually exclusive genotypes identified as A, B, C, D, E, and F, and they are all equally likely. If 20 offspring are tested, find the probability of getting exactly 5 As, 4 Bs, 3 Cs, 2 Ds, 3 Es, and 3 Fs by expanding the above expression so that it applies to 6 types of outcomes instead of only 3.

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n! (x1)!(x2)! (x3)! P