discrete mathematics

Question: The sides AB, BC, CA of a triangle ABC have 3, 4 and 5 interior points respectively on them. Find the number of triangles that can be drawn using these points as vertices. Answer: The points 3+4+5=12 points lie in a plane. To construct a triangle, we require three non-collinea..

Question: vi) (n! + 1) is not divisible by any natural number between 2 and n. vii) Simplify Answer: ..

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

Question: Find n, if P(n-1,3): P(n+1,3):: 5 : 12. Answer: n = 8 (as n cannot be a fraction..

Question: There are three different rings to be worn in 5 fingers with at most one in each finger. In how many ways can this be done? Answer: For the first ring, there are 4 options as one finger cannot have more than one ring. The remaining two fingers will have 3 and 2 options respect..

Question: Twelve students are participating in a competition. In how many ways can the first 3 prizes be won? Answer: Number of students participating in the competition = 12 The number of ways in which the first three prizes can be won = P (12,3) = 12 x 11 x 10 = 1320 Hence, 12 student..

Question: A sportsteam of 11 students is to be constituted choosing at least 5 from class XI and 5 at least from XII. If there are 20 students in each of these classes, in how many ways can the team be constituted? Answer: Number of students in each class is 20. Total number of selec..

Question: A committee of 6 is chosen from 10 men and 7 women so as to contain atleast 3 men and 2 women. In how many different ways can this be done, if two particular women refuse to serve on the same committee? Answer: Let the two ladies who refuse to work on the same committee be d..

Question: Five balls of different colours are to be placed in three boxes of different sizes. Each box can hold all five balls. In how many different ways can we place the balls so that no box remains empty? Answer: Given 5 balls can be placed in 3 boxes as follows: i. 1 ball can be pl..

Question: Find the number of diagonals in a polygon of n sides. Answer: In a polygon, no three points are collinear. To draw a line, we require two distinct points. The polygon of n sides has n distinct points. Number of diagonals that can be drawn ..