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12 Sep 2022, 13:50
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Bunuel
I need some help with this one, please. I have come up with 16 as the answer given the following:
with there being 2 different types of cars, and the family needing a combination of 3, there are a total of 4 possibilities:
AAA
BBB
AAB
ABB
if this were a permutation problem then I could understand how you arrive at 8 permutations of cars, but I only get the 4.
can anyone explain?
12 Sep 2022, 13:53
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Bunuel
I need some help with this one, please. I have come up with 16 as the answer given the following:
with there being 2 different types of cars, and the family needing a combination of 3, there are a total of 4 possibilities:
AAA
BBB
AAB
ABB
if this were a permutation problem then I would arrive at 8 possibilities. Can anyone explian?
02 Oct 2022, 05:07
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My approach:
We have total 8 cars, model A (blue, black, red, and green) & model B (blue, black, red, and green).
We can select cars in two ways:
1) 3 cars from model A (blue, black, red, and green) & 0 cars from model B (blue, black, red, and green) or 0 cars from model A (blue, black, red, and green) & 3 cars from model B (blue, black, red, and green).
2) 1 car from model A (blue, black, red, and green) & 2 cars from model B (blue, black, red, and green) or 2 car from model A (blue, black, red, and green) & 1 cars from model B (blue, black, red, and green)
Now selection
For 1) : 4C3*4C0 + 4C3*4C0 = 2* 4C3 = 8
For 2) : 4C1*3C2 + 4C1*3C2 = 2* 4C1*3C2 = 24 (3C2 coz we are only left with three options after choosing one car from other group)
Hence answer = 8+24 = 32
We have total 8 cars, model A (blue, black, red, and green) & model B (blue, black, red, and green).
We can select cars in two ways:
1) 3 cars from model A (blue, black, red, and green) & 0 cars from model B (blue, black, red, and green) or 0 cars from model A (blue, black, red, and green) & 3 cars from model B (blue, black, red, and green).
2) 1 car from model A (blue, black, red, and green) & 2 cars from model B (blue, black, red, and green) or 2 car from model A (blue, black, red, and green) & 1 cars from model B (blue, black, red, and green)
Now selection
For 1) : 4C3*4C0 + 4C3*4C0 = 2* 4C3 = 8
For 2) : 4C1*3C2 + 4C1*3C2 = 2* 4C1*3C2 = 24 (3C2 coz we are only left with three options after choosing one car from other group)
Hence answer = 8+24 = 32
