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?

- 720
- 480
- 360
- 350

720

Try upto 40 hours for free

Learn from the best!

Online Batches Available Now!

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 ^{6}C_{3} ways. We can select the one that is being repeated out of the three outcomes in ^{3}C_{1} 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 ^{6}C_{3} * ^{3}C_{1} * \\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?"**

Choice A is the correct answer.

CAT 2021

Enroll at

44,000/-

Online Classroom Batches Starting Now!

1. Digit Numbers | CAT Permutation and Combination | CAT Coaching Online

2. Numbers with Distinct Digits | CAT Permutation and Combination | CAT Coaching Online

3. Alphabetical Order | CAT Permutation and Combination | CAT Coaching Online

4. Geometric Progression | CAT Permutation and Combination | CAT Coaching Online

5. Bayes Theorem | CAT Permutation and Combination | CAT Coaching Online

2. Numbers with Distinct Digits | CAT Permutation and Combination | CAT Coaching Online

3. Alphabetical Order | CAT Permutation and Combination | CAT Coaching Online

4. Geometric Progression | CAT Permutation and Combination | CAT Coaching Online

5. Bayes Theorem | CAT Permutation and Combination | CAT Coaching Online

6. Rearranging Letters | CAT Permutation and Combination | CAT Coaching Online

7. Possible Integer Solutions | CAT Permutation and Combination | CAT Coaching Online

8. Rearrangement of Letters | CAT Permutation and Combination | CAT Coaching Online

9. Number Theory | CAT Permutation and Combination | CAT Coaching Online

10. Distribution | CAT Permutation and Combination | CAT Coaching Online

7. Possible Integer Solutions | CAT Permutation and Combination | CAT Coaching Online

8. Rearrangement of Letters | CAT Permutation and Combination | CAT Coaching Online

9. Number Theory | CAT Permutation and Combination | CAT Coaching Online

10. Distribution | CAT Permutation and Combination | CAT Coaching Online

Copyrights © All Rights Reserved by 2IIM.com - A Fermat Education Initiative.

Privacy Policy | Terms & Conditions

CAT^{®} (Common Admission Test) is a registered trademark of the Indian Institutes of Management. This website is not endorsed or approved by IIMs.

2IIM Online CAT Coaching

A Fermat Education Initiative,

58/16, Indira Gandhi Street,

Kaveri Rangan Nagar, Saligramam, Chennai 600 093

**Phone:** (91) 44 4505 8484

**Mobile:** (91) 99626 48484

**WhatsApp:** WhatsApp Now

**Email: **prep@2iim.com