# Calculate the probability for 2 different digits in 4 cells.

1. Jun 12, 2007

### yevi

The set S={1,2,3,4}, there are 4 cells.
What is the probability for 2 different digits (from S) to appear in 4 cells?
Example:

1,1,1,2 =>good
3,4,4,3 =>good
2,4,2,2 =>good

1,2,3,4 =>not good
1,2,3,3 =>not good
1,1,1,1=>not good

2. Jun 12, 2007

### matt grime

Count those where you have 1 of one element 3 of another, and then 2 each of two elements.

3. Jun 12, 2007

### yevi

Well, the 3 elements:

(4*3*2*3)/4^4

4 possibilities to choose first number, 3 possibilities to choose second number,
2 possibilities to choose third number and 3 possibilities to choose last number that has to be one of previous 3.

Is it right ?

4. Jun 12, 2007

### matt grime

Doesn't seem at all right to me.

5. Jun 25, 2007

### ssd

This appears to be a home task. Since you have not informed that you got the solution, I am giving a broader hint.
1st select the two to appear in the cells--- in 4C2 ways.
For each of such choice find the no. of possible arrangements for the following cases.
1/ both of them is arising twice
2/ A specific no. of them arising thrice and the other once (and multiply this by 2,why?)