CAT 2025 Lesson : Class Discussion: Modern Maths - Permutations & Combinations: 17 to 24

CLASS DISCUSSION - Permutations & Combinations

Question 17

In how many different ways can 3 or more of 15 identical balls be placed in 3 bags - A, B and C?

Answer: 445

Question 18

A 2 x 2 grid has to be coloured using 5 colours that are available. In how many different ways can you colour the grid such that no two adjacent grids have the same colour?

Answer: 260

Question 19

How many 3-digit numbers are there, for which the product of their digits is more than 2 but less than 7?
[CAT 2020 S1]

Answer: 21

Question 20

How many 4-digit numbers, each greater than 1000 and each having all four digits distinct, are there with 7 coming before 3?
[CAT 2020 S2]

Answer: 315

Question 21

In how many ways can 8 people sit around 2 identical round tables with 4 seats each (wherein both the tables are at the diametric ends of a rotating circular platform and the seats on each of the tables are equidistant from their adjacent seats)?

Answer: 1260

Question 22

In how many different ways can the letters of the word POLLUTION be rearranged such that the vowels occupy odd positions and the word does not begin with a 'P'?

Answer: 3456

Question 23

What is the maximum number of intersection points that we can get from 8 straight lines of which 4 are concurrent and 6 circles (with different radii) of which 2 are concentric?

Answer: 147

Question 24

10 members of a club are to sit around a round table and elect the next president. Ram and Shyam are the current president and vice-president and, therefore, have to sit next to each other. Lalitha, Meena and Naren are from a rival group who want to sit next to each other in such a way that none of them sit next to Ram or Shyam. In how many different ways can the 10 members be seated?

Answer: 5760

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