7 cars are parked side-by-side. 4 of them are black. How many different ways are there of arranging the cars so that the 4 black cars are parked next to each other?

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We have 7 cars parked side-by-side and 4 of them are black. To work out the number of ways the black cars can be parked next to each other, we proceed as follows:

First, we need to use a formula for choosing r items in a row out of n (r<=n).

This is n - r + 1

Because there is the first way, eg in the case of 4

b b b b . . .

and then n - r more ways as we shift to the right by 1...

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