jainvineet wrote:
Titleist wrote:
Good explanation. thanks.
I guess the number of steps can be reduced if we find the opposite first:
That is, find all combinations when two persons are ALWAYS together:
to chose 2M 4W, number of such arrangements will be:
6C0 * 5C4 = 5
{Number of combinations of n different things taken r at a time when p particular things always occur is n -pCr -p. }
similarly, to chose 3M 3W, number of arrangement when two men always together:
6C1 * 5C3 = 60
Total such combinations : 60 + 5 = 65
We need to subtract this from all arrangements (700 : see fresinha2 post below) to get required number:
700 - 65 = 635
I like this approach! !
Here is my confusion - Let us try to solve a simpler question
What are the combinations out of a group of 8 men, taken 3 at a time and two people always together.
so from your approach it is 8-2 C 3-2 => 6 C 1 = 6.
Now see it like this
ABCDEF XY are people X and Y always together. Conside X and Y one as Z.
Case 1 - when XY are not in the group selected Then 6 C 3 (3 people out of ABCDEF)
Case 2 when XY are in group then 6 C 1 ( 1 out of ABCDEF)
So the formula which you gave assumes that XY will always be in group.
I think less sleep is the root cause of all this
[/quote]
Yes you are correct - that is why you
must subtract the number in which people are
Always together from
the total possible number of combinations to get the number when the two people are
never together.
If we take your question and change it to "What are the combinations out of a group of 8 men, taken 3 at a time and two people are
never together."
It would be 8C3-6C1=50 possible combinations
Hope this clarifies Jain
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