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Out of six coins, four coins are tossed simultaneously.

The number of possible outcomes where at most three of the coins turn up as heads is ______.
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The question requires you to find number of the outcomes in which at most 3 coins turn up as heads.

i.e., 0 coins turn heads or 1 coin turns head or 2 coins turn heads or 3 coins turn heads.

The number of outcomes in which 0 coins turn heads is 6C0 = 1 outcome
The number of outcomes in which 1 coin turns head is  6C1 =  6 outcomes
The number of outcomes in which 2 coins turn heads is 6C2 = 15 outcomes
The number of outcomes in which 3 coins turn heads is 6C0 =  20 outcomes.

Therefore, total number of outcomes =1+6+15+20= 42 outcomes.

Answer:

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