A not so simple, simple head tails question

[Fussycarp]

I am stuck on a what should be a simple coin flip problem. *Out of the 64 different combinations of flipping 6 coins ; how many will only have 3 heads and 3 tails in any order?*

I am stuck on the resolving 3h and 3t. What is throwing me is that they say order doesn't matter. I even tried the brute-force attack, but only got 10.

Please help

Thanks

 

[Dr.Peterson]

I am stuck on a what should be a simple coin flip problem. *Out of the 64 different combinations of flipping 6 coins ; how many will only have 3 heads and 3 tails in any order?*

I am stuck on the resolving 3h and 3t. What is throwing me is that they say order doesn't matter. I even tried the brute-force attack, but only got 10.

Please help

Thanks

Do you know anything about permutations and combinations? How many ways are there to choose 3 of the 6 flips to be heads?

 

[pka]

*Out of the 64 different combinations of flipping 6 coins ; how many will only have 3 heads and 3 tails in any order?*

You want to know how many ways there are to rearrange the string [imath]\mathrm{HHHTTT}[/imath]
The string [imath]\mathrm{MISSISSIPPI}[/imath] can be rearranged in [imath]\dfrac{11!}{(4!)(4!)(2!)}[/imath] ways.
Apply that same idea to [imath]\mathrm{HHHTTT}[/imath]

 

[Deleted member 4993]

I am stuck on a what should be a simple coin flip problem. *Out of the 64 different combinations of flipping 6 coins ; how many will only have 3 heads and 3 tails in any order?*

I am stuck on the resolving 3h and 3t. What is throwing me is that they say order doesn't matter. I even tried the brute-force attack, but only got 10.

Please help

Thanks

When you have two coins, how many ways can you flip - 1H1T?

When you have four coins, how many ways can you flip - 2H2T?

When you have six coins, how many ways can you flip - 3H3T?

 

[Steven G]

I even tried the brute-force attack, but only got 10.

You got only about half (or maybe exactly half) of them with brute-force. Come on, you can do better than that! Please try again using some pattern.
1)Put 3 Ts at end (how many ways)
2) Put 2 Ts at end (how many ways)
3) Put 1 T at end
4) Put 0 Ts at end

 

[Harry_the_cat]

Have you learnt anything about the binomial distribution?

 

[Fussycarp]

You got only about half (or maybe exactly half) of them with brute-force. Come on, you can do better than that! Please try again using some pattern.
1)Put 3 Ts at end (how many ways)
2) Put 2 Ts at end (how many ways)
3) Put 1 T at end
4) Put 0 Ts at end

That worked. Thx. I just couldn't visualize what I needed. I had a brain clog. Now unstuck! Thanks

 

[Steven G]

That worked. Thx. I just couldn't visualize what I needed. I had a brain clog. Now unstuck! Thanks

So how many did you get? Do you also see how to use combinatorics to get the answer as described above?

 

[Fussycarp]

So how many did you get? Do you also see how to use combinatorics to get the answer as described above?

Yes, 20 combinations. 31.25 % of 64 total possibilities. I still would like to see the breakdown of the solution....well and understand it.

 

[Dr.Peterson]

I still would like to see the breakdown of the solution....well and understand it.

We've offered several suggestions of ways to calculate this without brute force, and understand why the answer is what it is; but you haven't told us anything about what you know beyond just listing, so it's hard to offer further help.

If you would tell us how much you have learned of combinations and permutations, the binomial distribution, or anything else, we can help you use what you know.