- #1

diracdelta

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## Homework Statement

Four balls are distributed randomly and independently into 4 cells.

What is probability that:

a) In every cell there is exactly one ball?

b) All four balls be in one cell?

c)Two balls in one cell ( any) , other two balls in other cell (any)?

(assume that the balls are different one from each other)

## The Attempt at a Solution

[/B]

For a)

P=4! / (4^4)

4! because there is 4! ways that we could distribute them, and 4^4 is all possible ways to distribute balls.

b)

[tex]\frac{\binom{4}{1} \cdot 4!}{4^{4}}[/tex]

Out of four cells i choose one where i will put them in, and since balls are not the same 4! to permutate them all

c)

[tex]\frac{\binom{4}{1} \cdot \frac{4!}{2!}\cdot \binom{3}{1}\frac{2!}{2!}}{4^{4}}[/tex]

Out of four cells choos one where i will put two balls and out of three cells choose one where i will put two balls.

Is this ok?