A political sience club consists of 25 members, 10 are freshmen and 15 are sopho
ID: 3133545 • Letter: A
Question
A political sience club consists of 25 members, 10 are freshmen and 15 are sophomores.
a. if the club is having an election for president, vice-president and second vice-president, how many different slates of candidates are possible if all member are eligible to be elected?
b. in the previous question, if only sophomores are eligible to run for these how many slates are possible?
c. if a team of five is being chose to participate in a debate with another college, how many teams are possible if all members are eligible?
d. in the previous question, how many choices are possible if the debate team must have 3 sophomores and 2 freshmen?
Explanation / Answer
A) WE HAVE TOTAL 25 MEMBER
AND IF ALL THE MEMBERS ARE ALLOWED TO CONTEST FOR ALL THE POST THEN FOR EACH POST THERE WILL BE 25 DIFFERENT SLATES
AS IN THIS PART WE HAVE TOTAL 3 POST THEREFORE TOTAL SLATES REQUIRED = 3*25 = 75
B) NOW IN THISS ONLY 15 ARE ALLOWED AND THE LECTION WILL BE FOR 3 POST
NOW EACH POST WILL HAVE 15 DIFFERENT SLATES
THEREFORE THE TOTAL SLATES REQUIRED = 3*15 = 45
C) NOW OUT OF THE TOTAL 25
A TEAM FOR 5 IS TO BE CHOOSEN
THEREFORE THE TOTAL WAYS IN THIS CAN BE DONE = 25C5 = 25!/(5!*20!) = 53130
D) IF WE HAVE TO CHOOSE 5 MEMBER TEAM FROM TWO DIFFERENT GROUPS
LIKE 3 FROM SOPHOMORES AND 2 FRESHMEN THEN THE TOTAL WAYS TO DO THIS WILL BE = 15C3*10C2 = [15!/(3!*12!)]*[(10!/(2!*8!)] = 20475.