Posted by Emily on Wednesday, February 17, 2010 at 10:00pm.
Let's say Bob is in both clubs. There are 11 other people.
Two cases: Bob is on the committee, or not:
a) Bob included:
First choose him, then choose any 3 of the other 11, since both clubs are represented by Bob:
11C3 ways to do that.
b) Bob excluded:
Now start with 11C4 (committees made up of the other 11 people).
Subtract 4C4 = 1 way with all 4 others from the camera club,
and 7C4 = 35 ways with 4 others from the math club.
11C3 + 11C4 - 1 - 7C4 = 165 + 330 - 1 - 35 = 459
Or we could say:
there are 12C4 total committees ( = 495 = 165 + 300 )
not worrying about Bob, and then just subtract the 1 which is the 4 camera club members
who are not Bob and the 35, which is the same for the math club.
Let's say Bob is in both clubs. There are 11 other people.
Two cases: Bob is on the committee, or not:
a) Bob included:
First choose him, then choose any 3 of the other 11, since both clubs are represented by Bob:
11C3 ways to do that.
b) Bob excluded:
Now start with 11C4 (committees made up of the other 11 people).
Subtract 4C4 = 1 way with all 4 others from the camera club,
and 7C4 = 35 ways with 4 others from the math club.
11C3 + 11C4 - 1 - 7C4 = 165 + 330 - 1 - 35 = 459
Or we could say:
there are 12C4 total committees ( = 495 = 165 + 300 )
not worrying about Bob, and then just subtract the 1 which is the 4 camera club members
who are not Bob and the 35, which is the same for the math club.
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