Possible Six-Flip Results

Probability Level 2

When 6 6 indistinguishable fair coins are thrown, how many different outcomes are there?

Details and Assumptions:

  • Two outcomes are the same if they contain the same number of heads.


The answer is 7.

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Arron Kau by Arron Kau

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4 solutions

Emmanuel David
Mar 30, 2015

This is how I got it.

HHHHHH

HHHHHT

HHHHTT

HHHTTT

HHTTTT

HTTTTT

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30 Helpful 2 Interesting 5 Brilliant 1 Confused

You can have 0 heads, 1 head, 2 heads...6 heads:and because we count a specific number of heads, each of these is an outcome. That makes 7. And there I was, making up answers around 64. Silly me. Read the question!

27 Helpful 0 Interesting 1 Brilliant 1 Confused

but it matters that on which coin we are getting heads. So correct ans will be 2 raised to 6 that is 64

Prashant Khatokar - 6 years, 3 months ago

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It is mentioned in the question that "2 outcomes are same if they have the same number of heads". So the correct asnwer will be 7. If this condition were not mentioned then the correct answer would have been 64

souptikji sen - 6 years, 2 months ago
Vanice Yee
Oct 6, 2015

Indistinguishable automatically rules out order, because you cannot tell which one is which. Since there are six coins that means the answer cannot be less than six. Finally, there are two sides to a coin which means one will repeat for the other side of the coin, so I + 1. Let me know if there is anything wrong with my logic.

6 Helpful 0 Interesting 0 Brilliant 1 Confused
Bostang Palaguna
Aug 17, 2020

since we can't distinguish the coins, we should only care about how many Heads or Tails exist:

the cases are: 0 tail, 1 tail, 2 tails, ... , 6 tails ⇒ \Rightarrow in total, there are 7 \boxed {7} cases.

2 Helpful 0 Interesting 0 Brilliant 1 Confused

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