# CAT Online Live Classes

Permutation Probability

### Concepts discussed on September 9, 2017

#### Combinatorics - Permutation Probability

Welcome to the live session of Permutation Probability. The concepts and questions discussed on September 9, 2017 during the live session follow the embedded video. The video link next to each concept will take you to the start of the part of the video where that specific concept is discussed. Click the video embedded below to watch the entire session.

#### Easy Questions

1. In how many ways can we select three cards from a pack of cards such that all three belong to different suits?

2. A tosses a coin 11 times. What is the probability there will be more heads than tails?

3. #### Medium Questions

4. How many 6 digit numbers exist comprising only the digits 2 and 4 such that they are multiples of 12?

5. How many 4 digit numbers have the product of their digits equal to 48?

6. In how many ways can we re-arrange the letters of the word "APTITUDE" such that no two vowels are next to each other?

7. A die is rolled thrice, what is the probability that the product of the three rolls is greater than 100?

8. How many scalene triangles with integer sides exist such that the product of two of the sides is 12?

9. Set A has all factors of 1080. Set B has all factors of 2800. How many elements are present in A U B?

10. How many integral factors of 720 are not factors of 2310?

11. In how many ways can we arrange the letters of the word TWO-IIM such that no two vowels are together?

12. SET S = {1, 2, 3, 4, …. 12}. How many non-empty subsets of set S exist such that the product of the elements of the subset is an even number?

13. #### Tough Questions

14. If a class has 5 students, what is the probability that no two are born on the same day of the week?

15. $(x-2)(x-4)(x-6)(x-8)(x-10) …. (x-100) < 0$How many integer values can x take?