Question

Solve the following question and mark the best possible option.
Let A = { 3, 6, 9, 12, ......., 696, 699} & B = {7, 14, 21, .........., 287, 294}
Find no. of ordered pairs of (a, b) such that a ∈ A, b ∈ B, a ≠ b & a + b is odd.

Options

• 4879

• 4893

• 2436

• 2457

Answer 1

A has `699/3` = 233 elements of which 116 are even & 117 are odd.
B has `294/7= 42` elements out of which 21 are even & 21 are odd.
A∩B = { 21, 42, ........, 273, 294}
∴ n(A ∩ B) = 14
For choice of a & b, 2 cases arise:-
Case- I: a is even & b is odd.
No. of possible cases = `""^116C_1 xx ""^21C = 116 xx 21`

Case-II: a is odd & b is even:-
No. of possible cases = `""^117C_1 xx ""^21C` = 117 x 21
But there are 14 cases where a = b & a, b, x A∩B.
So, required answer = 116 x 21 + 117 x 21 - 14 = 4879.