Hi - I had a question regarding this problem. I understand that the answer is 3c2 * 3c2 = 9, but the way I originally did it also seems correct to me and I cannot figure out why my method is incorrect. Here was my logic:
- You for sure have to have the distribution center in Chicago, so we just need to figure out how to distribute 4 distribution centers
- Each of the east coast and the west coast needs a center and there are 3 ways to choose each. So, 3 * 3 * 1 so far.
- Finally, the last two centers can be located in any of the cities we haven't used and there are 4 cities still available. So, 4c2, which equals 3.
So, 1 * 3 * 3 * 3 = 27, which isn't even among the answer choices, so I originally picked D. Could anyone point out the flaw in my logic? Thank you.
- You for sure have to have the distribution center in Chicago, so we just need to figure out how to distribute 4 distribution centers
- Each of the east coast and the west coast needs a center and there are 3 ways to choose each. So, 3 * 3 * 1 so far.
- Finally, the last two centers can be located in any of the cities we haven't used and there are 4 cities still available. So, 4c2, which equals 3.
So, 1 * 3 * 3 * 3 = 27, which isn't even among the answer choices, so I originally picked D. Could anyone point out the flaw in my logic? Thank you.
