Combinatorics DPP - RACE 3 - Grouping and Circular permutations easy
Required theory: Grouping of objects and Circular Permutations . Q1 - In how many ways 20 different books can be distributed between 7 students such that 3 students receive 4 books each and the remaining students receive 2 books each. Solution: First find the ways of grouping them in the group sizes of 4,4,4,2,2,2,2. 20!/(4!.4!.4!.3!).(2!.2!.2!.2!.4!) Then we need find ways of labeling them under 7 different labels. 7! Multiply both to get the final answer: 7!.20!/(4!.4!.4!.3!).(2!.2!.2!.2!.4!) Q2 - In how many ways 5 boys and 4 girls can sit in straight line if 2 girls are together and the other 2 girls are also together but separated from the first 2. Solution : First arrange 5 boys: 5! Now there are 6 gaps, choose 2: 6C2 Now if you see carefully, the 4 girls can be arranged in any order in these 2 gaps, so 4! Finally: 5!.6C2.4! = 43200 Q3 - (i) In how many ways five people can be distributed in three different rooms if no room must be empty? Make groups ...
