combinations: committees chosen from council

[tsh44]

Hello, I would appreciate some help.

A town council consists of 8 memebrs including the mayor.

a) How many different committees of 4 can be chosen form this council?
b) How many of these commitees include th amyor?
c) How many do not include the mayor?

For part A I am not positive but I did the combination 9C4 and got 126 possible committees. If this is incorrect I would appreciate an explanation.

For part B i am not sure how that would work out. For part C I assume I subtract the answer from part B from part A. Please help. Thank you.

 

[Gene]

Very close.
a) Right formula, wrong value. The eight included the mayor so it is
8C4

c) If the mayor is to be excluded it becomes 7C4

b) You are correct about the subtraction.

As a cross check, if the mayor is definitly included, it becomes him and 7C3