A vessel of volume `V_0` contains `N` molecule of an ideal gas. Find the probability of `n` molecules getting into a certain separated part of the vessel of volume `V`. Examine, in particle, the case `V = V_0//2`.

A vessel of volume `V_0` contains `N` molecule of an ideal gas. Find t

1.	A vessel of volume `V_0` contains `N` molecule of an ideal gas. Find the probability of `n` molecules getting into a certain separated part of the vessel of volume `V`. Examine, in particle, the case `V = V_0//2`.
Answer» The probability of one molecule being confined to the marked volume is `p = (V)/(V_0)` We can choose this molecule in many `(N_(C_(1)))` ways. The probability that `n` molecules get confined to the marked volume is cearly `N_(C_n) p^n (1 - p)^(N - n) = (N !)/(n!(N - n)!) p^n (1 - p)^(N - n)`.

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A vessel of volume `V_0` contains `N` molecule of an ideal gas. Find the probability of `n` molecules getting into a certain separated part of the vessel of volume `V`. Examine, in particle, the case `V = V_0//2`.

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