If you flip a fair coin 6 times, what is the probability that you will get exactly 2 tails? Why the answer is $\frac{6 \choose 2 }{2^6} = 15/64$ and not $2^4 / 2^6 = 4$. So we say there are 6 outcomes. Total # of out...--prophetes.ai

If you flip a fair coin 6 times, what is the probability that you will get exactly 2 tails? Why the answer is $\frac{6 \choose 2 }{2^6} = 15/64$ and not $2^4 / 2^6 = 4$. So we say there are 6 outcomes. Total # of outcomes is $2^6$ since for each outcome we have two choices. Then we say 2 are tails. Then for 2 of outcomes we have only one choice and for rest 2 e.g $222*211 = 2^4$. So where is the mistake? Note: I understand "choose" argument and I answered this question correctly. I just then though of another "argument" which seems to be "okay", but which gives wrong result. I want to understand why it is wrong

"for the rest $2$ **e.g.** $2*2*2*2*1*1$"...

Exactly (e.g.=exempli gratia), and there are more examples.

For instance $2*1*2*1*2*2$ is another one.

How many in total? $$\binom62$$

This should explain the factor.