CAT Online Live Classes

Permutation Probability

Concepts discussed on July 14, 2018

Combinatorics - Permutation Probability

Welcome to the live session of Permutation Probability. The concepts and questions discussed on July 14, 2018 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.

Medium Questions

1. Sum of three Natural numbers a, b and c is 10. How many ordered triplets (a, b, c) exist?

2. In how many ways 11 identical toys be placed in 3 distinct boxes such that no box is empty?

3. If we listed all numbers from 100 to 10,000, how many times would the digit 3 be printed?

4. All numbers from 1 to 150 (in decimal system) are written in base 6 notation. How many of these will contain zero's?

5. I roll a die 4 times. In how many outcomes do we have two throws have the same number and the other two something different?

6. A bag contains 4 red and 3 black balls. A second bag contains 2 red and 3 black balls. One bag is selected at random. If from the selected bag one ball is drawn, then what is the probability that the ball drawn is red?

7. In how many ways can 6 boys be allotted into 5 rooms such that no room is empty and all 6 boys are accommodated?

8. Tough Questions

9. Sum of three Whole numbers a, b and c is 10. How many ordered triplets (a, b, c) exist?

10. a, b, c are three distinct integers from 2 to 10 (both inclusive). Exactly one of ab, bc and ca is odd. abc is a multiple of 4. The arithmetic mean of a and b is an integer and so is the arithmetic mean of a, b and c. How many such triplets are possible (unordered triplets)?

11. I roll a die 4 times. In how many outcomes will each subsequent throw be greater that the previous one?