Formula for this combination problem

In summary, the conversation discusses the number of possible outcomes when flipping a coin n times, where the outcome must have an even number of the opposite side between two consecutive same sides or all the sides are the same. The accepted outcomes for n=3, 4, and 5 are listed as TTT, HHH, TTH, HHT, HTT, THH, TTTT, HHHH, HTTH, THHT, HHTT, TTHH, TTTTT, HHHHH, HTTHH, THHTT, TTHHT, HHTTH, TTTTH, TTTHH, HHHHT, HHHTT, HHTTT, TTHHH,
  • #1
rhonkie
2
0
Hi,

What is the number of possible outcomes of a flipped coin with the following property:
Let n be the number of times a coin is flipped, the outcome must be of the form that between two consecutive same side, there is an even number of the other side, or all are of one side...

For example
n=3,
The accepted outcome should be : TTT,HHH,TTH,HHT,HTT,THH. So I can't have an outcome like HTH or THT

n=4,
The accepted outcome should be : TTTT,HHHH,HTTH,THHT,HHTT,TTHH,TTTH, HHHT, HTTT, THHH.

n=5,
the accepted outcome should be: TTTTT, HHHHH, HTTHH, THHTT, TTHHT, HHTTH, TTTTH, TTTHH, HHHHT, HHHTT, HHTTT, TTHHH,HTTTT, THHHH .
So I know that there can only be 6, 10 and 14 possible outcomes for n = 3, 4 and 5 respectively for flipping a coin five time for this problem. How about for an arbitrary n.

I do hope you understand how I've explained this problem. Any reply would be greatly appreciated.
 
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  • #2
I don't really understand it... TTH does not have an even number of one side between two of the other side like THHT does, for example; nor does is consist of three of the same side like TTT does. So why again is this allowed?
 
  • #3
Well, one can't really see this allowable pattern for n less than or equal to 3. Perhaps what I should have said is that the following sort of outcome is not allowed:

between two consecutive same sides, odd number of the other sides is not counted as accepted outcome. Every other outcomes are allowed.

Sorry for the ambiguity in my post. And thanks in advance
 

1. What is the formula for a combination problem?

The formula for a combination problem is nCr = n!/(r!(n-r)!), where n represents the total number of items and r represents the number of items being chosen.

2. How do I know when to use the combination formula?

The combination formula is used when the order of the items being chosen does not matter. This is different from a permutation problem, where the order does matter.

3. Can the combination formula be used for both small and large numbers?

Yes, the combination formula can be used for both small and large numbers. However, for large numbers, it is often easier to use a calculator or computer to calculate the factorial values.

4. Are there any special cases when using the combination formula?

Yes, there are a few special cases when using the combination formula. One is when r = 0, which results in nC0 = 1. Another is when r = n, which results in nCn = 1. Lastly, when n = 0, all combinations are considered to be 0.

5. Can the combination formula be applied to real-life situations?

Yes, the combination formula can be applied to real-life situations, such as calculating the number of possible combinations for a lock with a set number of digits or determining the number of different meal combinations at a restaurant with a fixed menu. It is a useful tool in various fields of science, including statistics, genetics, and economics.

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