Question

A president and a treasurer are to be chosen from a student club consisting of 50 people. How many different choices of officers are possible if

a. there are no restrictions
b. A will serve only if he is president
c. B and C will serve together or not at all?

Answer 1

if there are no restrictions then you have 50 choices for president, and once that is chosen, 49 choices left for treasurer
by the counting principle the total number of choices is \(50\times 49\)

Answer 2

if A will only serve as president, then if A is chosen as president there are 49 choices left for treasurer
if A is not chosen as president, then you have 49 choices for president and subsequently 48 for treasurer for a total of \(49\times 48\) possibilities, and therefore \(49\times 48+49\) possible combinations

Answer 3

B and C will serve together or not at all
if they are chosen, then two possibilities, B president, C treasurer or vice versa
if they are not chosen then \(48\) possibilities for president, and then \(47\) for treasurer
for at total of \(48\times 47+2\)

Answer 4

satellite73 i have one more problem... I dont want solution just some clarification... can i ask it here or post a new one??

Answer 5

post a new one i will look

Answer 6

ok

Answer 7

give me 5 min.