A bag contains 7 white balls and 4 black balls. 4 balls are taken from the bag. Does it matter if the balls are taken 1 at a time or all 4 are "grabbed" all at once? Count how many ways there are at least 3 white balls.


I don't think the way the balls are taken out matters, but I'm confused about the second question.

I think you would consider the 3 white balls as "locked" and then select the remaining ball by doing C(3, 1) or C(10, 1).


Thank you!

 Mar 22, 2020

In this case, I think it does matter whether you take it one at a time or not...


I think you have to take it one at a time....

 Mar 22, 2020

If all you care about is the final result, then it doesn't make any difference if you grab them all at one time or take them one-by-one.


If the white balls are somehow distinguishable from each other and the same for the black balls (as in the case where you select 4 girls from a total of 7 girls and one boy from a total of 4 boys to get a committee of 4 persons), then the number of ways would be this:

To get 3 white balls and one black ball:  7C3 x 4C1  =  35 x 4  =  140

To get 4 white balls and no black balls:  7C4 x 4C0  =  35 x 1  =  35

Adding:  140 + 35  =  175

 Mar 22, 2020

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