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Suppose 20 fair indistinguishable dice are tossed at once. Denote the sample space by S ( Note that the size of

the sample space is NOT 620 since the dice are not tossed in order!).

(a) Find the number of elements in S. [Hint: denote the number of i's observed by xi, i=1,...,6,andobservethatalwaysweshouldhavex1+x2+...+x6 =20.]

(b) What is the probability that none of the dice are a 6? (

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