# Questionbank: Permutation and Probability

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Rolling a die to get the desired outcome isn't easy as you think!!

## Rolling a Die

Q.21: I roll a die four times. In how many outcomes do we have two throws have the same number and the other two something different?
1. 720
2. 480
3. 360
4. 350

Choice A. 720

## Detailed Solution

If we want to have two throws to have the same outcome and the other two being something different, we are essentially looking for three different outcomes in each throw.

We can have three different outcomes in each throw in 6C3 ways. We can select the one that is being repeated out of the three outcomes in 3C1 ways.

And then, they can be arranged in 4!/2! ways, since there are totally 4 throws out of which 2 are repeated. So, Totally , we can do this in 6C3 * 3C1 *${\frac{4!}{2!}}$ = ${\frac{(4*5*6)}{6}}$* 3 *12 = 20*3*12 = 720 ways.

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