In how many ways can 5 distinct balls be dist | vedclass

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(B) The problem is equivalent to finding the number of onto functions from a set of $5$ elements to a set of $3$ elements.Using the Principle of Inclu

Vedclass · Accepted Answer

$150$

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(B) The problem is equivalent to finding the number of onto functions from a set of $5$ elements to a set of $3$ elements.Using the Principle of Inclusion-Exclusion,the number of ways is given by $3^5 - \binom{3}{1} 	imes 2^5 + \binom{3}{2} 	imes 1^5$.Calculating the values: $3^5 = 243$,$2^5 = 32$,and $1^5 = 1$.Number of ways = $243 - 3 	imes 32 + 3 	imes 1$.Number of ways = $243 - 96 + 3 = 150$.

In how many ways can $5$ distinct balls be distributed among $3$ persons such that each person receives at least one ball?

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