If 4 marbles are drawn at random all at once from a bag containing 8 white and 6 black marbles. in how many ways can we draw the 4 marbles so that 2 will be white and 2 will be black?

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Mathematics

11 December, 09:09

If 4 marbles are drawn at random all at once from a bag containing 8 white and 6 black marbles. in how many ways can we draw the 4 marbles so that 2 will be white and 2 will be black?

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Haney · Answer 1

You started out as if it was going to be a probability problem, but it turned out to be a simple binary counting problem.

It really doesn't matter how many of each color are in the bag, or how many marbles there are in the bag all together. I think you're just asking how many ways there are to pull out two white ones and two black ones. That's exactly the same question as "How many 4-bit binary numbers can be written with two 1's and two 0's?"

It's easy to draw up that list. You start out like this:

0011, 0101, 1001, 0110, 1010, 1100.

Gosh. I just wanted to start out doing the list, but I think that's all of them.

There are six (6) ways.

WWBB, WBWB, BWWB, WBBW, BWBW, and BBWW.