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The number of ways 6 heads and 4 tails can occur is equal to the number of permutations of 10 items taken 6 at a time. This can be calculated using the formula for permutations:
P(10,6) = 10!/(10-6)! = 10!/(4!) = 5040
Therefore, there are 5040 ways 6 heads and 4 tails can occur when a coin is tossed ten times.