math questions

Question 1 - Question: From a class of 32 students, 4 are to be chosen for a competition. In how many ways can this be done? Answer: We are to select 4 students from 32. This selection can done ..

Question: A candidate is required to answer 6 out of 10 questions, which are divided into two groups, each containing 5 questions, and he is not permitted to attempt more than 4 from each group. In how many ways can he make his choice? Answer: ..

Question: Answer: Aliter: ..

Question: Answer: ..

Question: When n = 5 and r = 2, find the values of Answer: i) ii) ..

Question: Answer: ..

Question: Answer: ..

Question: Convert the following into factorials: i) 5.6.7.8.9.10 ii) 4.6.8.10.12 Answer: i) ii) ..

Question: Prove that n!(n + 2) = n! + (n + 1)!. Answer: L.H.S = n!(n + 2) = n![(n+1)+1] ..

Question: Find the number of triangles that can be drawn through 12 distinct points, no three of which are collinear. Answer: To draw a triangle, we require three non-collinear points. Hence, the number of triangles that can be drawn is ..