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In mastermind we have 8 different colours and 4 pins. how many of these codes will have...

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In mastermind we have 8 different colours and 4 pins. how many of these codes will have 4 different colours?

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You choose the first pin.  8 options.

You choose the 2nd pin.  7 options (you don't want to repeat the first color).

So for the first two pins, you have 56 combos possible.

You choose the 3rd pin. 6 options.

You choose the 4th pin. 5 options.

So there are `8*7*6*5` = 1680 ways to choose 4 pins (in specific positions) such that no color is repeated.

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