Problem 27 (counting committees)This is given by the multinomial coefficient123,4,5= 27720Problem 28 (divisions of teachers)If we decide to sendn1teachers to school one andn2teachers to school two, etc. then thetotal number of unique assignments of (n1, n2, n3, n4) number of teachers to the four schoolsis given by8n1, n2, n3, n4.Since we want the total number of divisions, we must sum this result for all possible combi-nations ofni, orn1+n2+n3+n4=88n1, n2, n3, n4= (1 + 1 + 1 + 1)8= 65536,possible divisions.If each school must receive two in each school, then we are looking for82,2,2,2=8!(2!)4= 2520,orderings.Problem 29 (dividing weight lifters)
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