3. In a local election, there are four candidates for mayor, five candidates for

Question

3. In a local election, there are four candidates for mayor, five candidates for city treasurer, and two candidates for county attorney (a) In how many ways can a voter mark her ballot for all three of these offices? for any or all of these offices? 4. (a) How many ways are there to divide the 15 faculty members of a department into five committees of size 3, if each faculty member muist serve on one and only one committee (b) What if every faculty member may serve on any number of committees (i.e. anywhere from none up to all five)?

Explanation / Answer

3 ans) given there are four candidates mayor

five candiadtes are for city treasurer

two candiates for county attorney

a) num of ways can a voter mark her ballot all three of these offices = 4.5*2 =40 ways

b) no of ways not voting for a candidates =5*6*3= 90 ways

4) a) number of ways in each and faculty member serve on one and only one comitte is

15* 5c3

b) every faculty member may serve on any number of comittes is 15c5

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