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).
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....
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