If a and b are any two distinct numbers belonging to the set {1,2,......100}, then the number of pairs (a, b) such that product of a and b is divisible by 3 is 5478 2. 5278 3. 2739 3. 2639 5. 2837

Options

A. `5478`
B. `5278`
C. `2739`
D. `2639`

Answer

A

Explanation

If a and b are ………….
`S = {1, 2, 3,…..100}`
elements of `S` are of from `3n : 3,6,9,….00 rarr 33` number
`3n+1:1,4,7,…..100 rarr 34`
`3n+2:2,5,8….98 rarr 33`
If ab is to be divisible by 3 either a or b is divisible by 3 or both a and b are to be divisible by 3. The number of ways a and b can be
`=(.^(33)C_(2)+^(33)C_(1)xx^(34)C_(1)+^(33)C_(1))xx2`
`= 2739xx2=5478`