Question

A fair coin is tossed twice, the sample space is {HH, HT, TH, TT}, how can we calculate the number of combinations by using the formula n!/(n-k)!k! ??????

Answer 1

number of combination of ???

Answer 2

how to calculate the number of combinations of head & tail

Answer 3

like??

Answer 4

@experimentX acc' I am trying to know that how exactly we use this formula in such problem

Answer 5

to determine the sample space??

Answer 6

yes but not by using

Answer 7

the power set

Answer 8

at http://www-math.mit.edu/phase2/UJM/vol1/RMONTE-F.PDF the binomial coefficient starts after sample space but I don't understand it's relation with the given sample space

Answer 9

i guess
\[ \sum_{i=0}^{n} \binom{n}{i}\]

Answer 10

\( \large \binom{n}{i}\) gives the number of particular combination. like {HT}, {TH} they both are combination of H and T

Answer 11

@experimentX can you please tell me that what does it mean by
Note
that n and x must have the same parity because n-x = 2l.

Answer 12

it's in the link that I mentioned above

Answer 13

i mean in which page in which line??

Answer 14

on the second page (marked as 111) the last paragraph, start with "Now, there are"

Answer 15

what does mean by the parity? does it mean as the equality in amount if yes then 2l = 0

Answer 16

also what does mean by the x = n mod 2 in the first formula of 3rd page it comes after the paragraph that I mentioned above

Answer 17

looks like i have to look from the beginning ... it will take a bit more time!!

Answer 18

OK, it will be really great if you help me in understanding this concept

Answer 19

it would be great if i understand if i understand these concepts myself

Answer 20

I don't know that parity means ... the second formula relates
let 'q' be probability of left and 'p' be of right

to arrive at a point, you take l left steps and r right steps,
C(n,l) is the no of ways you can choose ,,, left and right steps out of total .. so \( C(n,l)
p^rq^l; \) gives you the probability to arrive at a particular step

Answer 21

if you take one step, you will never arrive at the place point ...
similar if you take two step ... you will never be at the adjacent place

x = n mod 2 is the condition for that probability, check out that table!!

Answer 22

thanks

Answer 23

@ 4. Taking a Step Further (3rd page) it says first return, what does it mean?

Answer 24

Looks like this got something to do with Catalan numbers ... i have known them but i am encountering catalan numbers for the first time

Answer 25

that means ... the drunk returns to the first step at 2n the step

Answer 26

gotta sleep .... interesting concept though!!