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The probability to get heads once is 1/2 as the coin is fair

The probability to get heads twice is 1/2x1/2

The probability to get heads three times is 1/2x1/2x1/2

The probability to get tails once is 1/2

The probability to get tails 5 times is (1/2)5

So the probability to get 3 heads when the coin is tossed 8 times is (1/2)3(1/2)5=(1/2)8 = 1/256

If you read carefully you'll understand that 3 heads and 5 tails has the same probability than any other outcome = 1/256

As the coin is fair, each side has the same probability to appear

So the probability to get 3 heads and 5 tails is the same as getting for instance 8 heads or 8 tails or 1 tails and 7 heads, and so on

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