Heads or tails? (Question from Feynman lectures)

[#neutrino]

I have been going through feynmans lectures on probability and have a few questions that i can't answer ; in the part regarding fluctuations he introduces us to tree diagrams(pascals triangle ) and gives an example regarding the toss of a coin
If we consider the no. Of tosses as n and no. Of heads as k then it can be given as
( n) n!
( k ) = ----
k!(n-k)!
I know that n! Represents n factorial and the fact that probability is generally
Given by
Probability = highest estimate of an event
----------------------------
Total no. Of events
However what i don't get is why do we multiply k! By (n-k)! Souldnt it be n! In the denominator and k! In the numerator ?
I know it has something to do with the triangle however unable to figure it out

 

[#neutrino]

I have been going through feynmans lectures on probability and have a few questions that i can't answer ; in the part regarding fluctuations he introduces us to tree diagrams(pascals triangle ) and gives an example regarding the toss of a coin
If we consider the no. Of tosses as n and no. Of heads as k then it can be given as
( n) n!
( k ) = ----
k!(n-k)!
I know that n! Represents n factorial and the fact that probability is generally
Given by
Probability = highest estimate of an event
----------------------------
Total no. Of events
However what i don't get is why do we multiply k! By (n-k)! Souldnt it be n! In the denominator and k! In the numerator ?
I know it has something to do with the triangle however unable to figure it out

The equation is (n)= n!
(k) -----
k!(

 

[#neutrino]

The equation is (n)= n!
-----
k!(n-k)!

 

[PeroK]

You're actually asking, I think, about how many ways you can get $k$ heads from $n$ coin tosses. And why the answer is $\frac{n!}{(n-k)! k!}$

You could start by taking $n = 5$, say, and counting all the ways you can get $k = 0, 1, 2, 3, 4$ and $5$.

Then see whether that fits the formula, and why.

 

[codelieb]

BTW (just in case anyone is interested), this was not Feynman's lecture, but Matt Sands' lecture. Feynman had to go out of town on some business for a week, so Matt Sands gave the lectures that became FLP Vol. I Chapters 5 and 6.