# Counting Problem - Coin Flip

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• Mar 8th 2010, 05:46 AM
sedemihcra
Counting 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?
• Mar 8th 2010, 05:56 AM
Archie Meade
Quote:

Originally Posted by sedemihcra
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?

What about the possibility of all 10 being tails?
• Mar 8th 2010, 06:03 AM
sedemihcra
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.
• Mar 8th 2010, 06:08 AM
Archie 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.
• Mar 8th 2010, 06:11 AM
sedemihcra
Thanks a bunch.