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06 Dec 2005, 16:43
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Here comes a combination question.
There are 18 employees in a firm; 10 managers and 8 programmers.
How many 3 member groups can you form if you have to;
a) Have at least 1 manager in each group
b) Have at least 1 programmer in each group.
Ie. MPP, PMM etc.
No answer choices available, lets see some working out!
There are 18 employees in a firm; 10 managers and 8 programmers.
How many 3 member groups can you form if you have to;
a) Have at least 1 manager in each group
b) Have at least 1 programmer in each group.
Ie. MPP, PMM etc.
No answer choices available, lets see some working out!
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06 Dec 2005, 17:07
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Before you pick members, assign 1 manager and 1 programmer to each group.
Picking 1 manager = 10C1
Picking 1 programmer = 8C1
Now, you already have 2 members (one manager and one programmer), and you need just one more member ( = any member is ok ) in each group.
There are 16 members remaining.
Picking 1 member(manager or programmer, ganz egal) = 16C1
10C1 * 8C1 * 16C1 = 80 * 16 = 1,280
Since ( Manager + Programmer + Any member ) group and ( Programmer + Manager + Any member ) group have to be counted as one, divide 1,280 by 2, which yields 640.
Picking 1 manager = 10C1
Picking 1 programmer = 8C1
Now, you already have 2 members (one manager and one programmer), and you need just one more member ( = any member is ok ) in each group.
There are 16 members remaining.
Picking 1 member(manager or programmer, ganz egal) = 16C1
10C1 * 8C1 * 16C1 = 80 * 16 = 1,280
Since ( Manager + Programmer + Any member ) group and ( Programmer + Manager + Any member ) group have to be counted as one, divide 1,280 by 2, which yields 640.
