From the set 1,2,3,4,5 two numbers ' a ' and ' b ' (a b) are chosen at random. The probability that a b is an integer is

Step-by-step solution

The total number of ways to choose two distinct numbers a and b from the set 1, 2, 3, 4, 5 is given by the number of permutations ⁵P₂ = 5 4 = 20 . We need to find the number of pairs (a, b) such that a b is an integer. This means a must be a multiple of b with a b . Listing the possible pairs (a, b) where a is a multiple of b and a b : If b = 1 , a can be 2, 3, 4, 5 (4 pairs). If b = 2 , a can be 4 (1 pair). If b = 3 , no a exists in the set such that a is a multiple of 3 and a 3 . If b = 4 , no a exists in the set