SOLUTION: There are 10 people in department A, 15 people in department B and 20 people in department C. How many committees of 6 members can be formed such that each department has at least

Question 499014: There are 10 people in department A, 15 people in department B and 20 people in department C. How many committees of 6 members can be formed such that each department has at least 1 member?
Answer by chessace(471) (Show Source): You can put this solution on YOUR website!
This is more complicated than it looks.
It can't be done as a single term, you have to add up a few items.
I learned one additional trick getting it right.
Because columns aren't easy with these fonts, I'll use ";" to separate them.
Pick; A; B; C; Sum(optional)
1; 10; 15; 20;
The trick: divide by 5 next lines until "*125".
1; 2; 3; 4;
2; 9; 21; 38;
3; 24; 91; 228;
4; 210; 1365; 4845;
Split; Amax; Bmax; Cmax; Sum
411; 42*12; 273*8; 969*6;
compute; 504; 2184; 5814; 8502
321; 24(84+114); 91(76+36); 228(27+42)
compute; 4752; 10192; 15732; 30676
222; 9*21*38 = 7182
Total; 411; 321; 222; Sum
; 8502; 30676; 7182; 46360
*125: 5,795,000 (the answer)
Note: Those possibilities using 3 from C are 33.9% of total.
Note 2: Even though answer is even # of 1000, there is no short cut because 5795 = 5*19*61 and 61 isn't going to show up in any factorial here.

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