A box contains 5 red, 4 white, and 6 blue balls. Two balls are drawn at random. Find the probability that they are both of the same color.
A manufacturer produces two types of products A and B, which require 2 hours and 3 hours respectively for production on machine I, and 4 hours and 2 hours respectively on machine II. The machine I has 20 hours and machine II has 18 hours available per week. The profit on each product of type A is ₹6 and on type B is ₹8. Formulate the problem as a linear programming problem to maximize the profit.
Find the equation of the plane passing through the point (1,−2,3) and perpendicular to the vector .