CAT Quantitative Aptitude Questions | CAT Permutation and Combination Questions

The question is from Permutation and Combination. This question is about rolling a die. We need to find out about a particular outcome of a die. This section hosts a number of questions which are on par with CAT questions in difficulty on CAT Permutation and Combination, and CAT Probability.

Question 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

Explanatory Answer

Method of solving this CAT Question from Permutation and Combination: Rolling a die to get the desired outcome isn't easy as you think!!

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.

The question is "In how many outcomes do we have two throws have the same number and the other two something different?"

Hence the answer is "720"

Choice A is the correct answer.