CAT 2025 Lesson : Class Discussion: Modern Maths - Permutations & Combinations: 9 to 16
Class Discussion: Permutations & Combinations
Question 9
You can either take a step ahead, behind, to the left or to the right. After 6 such steps, you are back to the same position. In how many different ways could you have done this?
Answer: 400
Question 10
The figure shows the plan of a town. The streets are at right angles to each other. A rectangular park (P) is situated inside the town with a diagonal road running through it. There is also a prohibited region (D) in the town. [CAT2008]
Neelam rides her bicycle from her house at A to her office at B, taking the shortest path. Then the number of possible shortest paths that she can choose is
60
75
45
90
72
Question 11
The figure shows the plan of a town. The streets are at right angles to each other. A rectangular park (P) is situated inside the town with a diagonal road running through it. There is also a prohibited region (D) in the town. [CAT2008]
Neelam rides her bicycle from her house at A to her club at C, via B taking the shortest path. Then the number of possible shortest paths that she can choose is
1170
630
792
1200
936
Question 12
If all the 6-letter words that can be formed by rearranging the letters of the word JUGGLE are arranged in alphabetical order, what is the rank of the word JUGGLE?
Answer: 235
Question 13
How many numbers with two or more digits can be formed with the digits 1, 2, 3, 4, 5, 6, 7, 8, 9, so that in every such number, each digit is used at most once and the digits appear in the ascending order? [CAT 2018 S1]
Answer: 502
Question 14
In how many ways can Ramu distribute 6 differently coloured pens to his 5 friends such that not more than 2 of them receive none of the pens?
Answer: 15000
Question 15
In a tournament, there are 43 junior level and 51 senior level participants. Each pair of juniors play one match. Each pair of seniors play one match. There is no junior versus senior match. The number of girl versus girl matches in junior level is 153, while the number of boy versus boy matches in senior level is 276. The number of matches a boy plays against a girl is [CAT 2018 S2]
Answer: 1098
Question 16
There are 15 identical balls and all of them need to be placed in 3 bags - A, B and C such that each of the bags contain at least one ball and exactly 1 of the bags contains an odd number of balls. In how many different ways can this be done?
Answer: 63
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