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the question is on probability. there are 18 balls,12 red and 6 white.six balls are drawn one by one without replacement.if atleast 4 are white,find the probability that next two draw will result in one red and one white. i dont need the solution as dis was a problem given in iit and i do hv its solution with me.but my doubt is, as its given that balls are drawn one by one should we write 6c1*5c1*4c1*3C1 or 6c4 taking all of them at a time. and do explain the reason plz

the question is on probability.


       there are 18 balls,12 red and 6 white.six balls are drawn one by one without replacement.if atleast 4 are white,find the probability that next two draw will result in one red and one white.


       i dont need the solution as dis was a problem given in iit and i do hv its solution with me.but my doubt is, as its given that balls are drawn one by one should we write 6c1*5c1*4c1*3C1 or 6c4 taking all of them at a time. and do explain the reason plz

Grade:12

1 Answers

Ashwin Muralidharan IIT Madras
290 Points
9 years ago

Hi Aishwarya,

 

It has to be 6C4.

Consider W1,W2,W3,....,W6 as six white balls.

 

If you say that you want to select four white balls, and if you say 6C1*5C1*4C1*3C1, then see how many cases you are repeating.

For example say first you selected W1, then W2, then W3, then W4. Now say in another case you are selecting W2, then W1, then W3, then W4. In both cases you have the same set of balls. But you would have counted it twice.

So the right way of selecting is 6C4.

 

Regards,

Ashwin (IIT Madras).

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