How many election outcomes in the race for class president a

How many election outcomes in the race for class president are there if there are five candidates and 40 students in the class and

(a) Every candidate receives at least two votes?

(b) One candidate receives at most one vote and all the others receive at least

two votes?

(c) No candidate receives a majority of the votes?

(d) Exactly three candidates tie for the most votes?

Solution

^a)Every candidate receives at least two votes?

after every candidate recieving two votes remaining 30 will be distributed among the five

so number of ways 30C₅

(c) No candidate receives a majority of the votes?

Here all the candidates recieving 8 votes each

number of ways = 40!/(8!)⁵