Can you explain it w/ the most detail as possible? Thank you so much!! Suppose t

Question

Can you explain it w/ the most detail as possible? Thank you so much!!

Suppose that an experiment can result in one of r possible outcomes, the ith outcome having probability pi, i = 1,...,r, ri=1 pi = 1. If n of these experiments are performed, and if the outcome of any one of the n does not affect the outcome of the other n- 1 experiments, then show that the probability that the first outcome appears X1 times, the second x2 times, and the rth xrtimes is n!/x1!x2! ... xr! Px11Px22 ... Pxrr when x1 + x2 + ... + xr = n This is known as the multinomial distribution.

Explanation / Answer

required probability=(p1+p2+p3+...pr)n

=n!/(x1!x2!....xr!)*(p1x1p2x2....prxr)

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