A coin is flipped 10 times. How many outcomes have at most 3 heads?

My best guess is

[C(10,3)]+[C(10,2)]+[C(10,1)] = 120 + 45 + 10 = 175 outcomes.

Is this the solution?

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- March 8th 2010, 06:46 AMsedemihcraCounting Problem - Coin Flip
A coin is flipped 10 times. How many outcomes have at most 3 heads?

My best guess is

[C(10,3)]+[C(10,2)]+[C(10,1)] = 120 + 45 + 10 = 175 outcomes.

Is this the solution? - March 8th 2010, 06:56 AMArchie Meade
- March 8th 2010, 07:03 AMsedemihcra
Never thought of having all of them being tails. I guess the solution would then be:

[C(10,3)]+[C(10,2)]+[C(10,1)] + [C(10,0)]

= 120 + 45 + 10 + 1

= 176 outcomes. - March 8th 2010, 07:08 AMArchie Meade
Yes.

If the question had been worded...

For outcomes involving "at least 1 head", how many outcomes contain

at most 3 heads...

your first answer was fine. - March 8th 2010, 07:11 AMsedemihcra
Thanks a bunch.