Combinatorics practice problems - RACE 1 - Easy
Q1 - There are nine students (5 boys & 4 girls) in the class. In how many ways: (1) Three distinct books can be distributed between two boys and one girl. A: 5C2 * 4C1 * 3! = 240 (2) Three distinct books can be distributed between three students in which at least one is boy. A: 3! * [5C1*4C2 + 5C2 * 4C1 + 5C3] = 480 (3) One book of Maths, two books of Physics and three books of Chemistry can be distributed (No student can get more than one book in same subject & books are distinct). A: 9C1 * 9C2 * 9C3 * 3! * 2! = 326592 Explanation: We have to choose 1 kid for Maths, 2 for Physics, 3 for Chemistry. Now let's say you gave 2 physics books to K1,K2. So 2! for counting number of ways. Similarly if Chemistry books C1,C2,C3 were given to K1,K2,K3 then again there are 3! different ways to do that. Q2 - How many arithmetic progressions with 10 terms are there, whose first term is in the set {1, 2, 3, 4} and whose common difference is in the set {3, 4, 5, 6, 7} ? A: 5*4 = 20 Q3 -...