the total number of ways of selecting two number from the set {1,2,3,4,…..3n} so that their sum divisible by 3 is equal to -

Options

A. `(2n^(2)-n)/(2)`
B. `(3n^(2)-n)/(2)`
C. `2n^(2)-n`
D. `3n^(2)-n`

Answer

B

Explanation

Given number can be rearranged as
` 1,4,7,.....,3n-2 to 3lamda-2`
`2,5,8,.....3n-1 to 3 lamda-1`
` 3,6,9,....,3nto 3lamda `
that means , we must take two number from last row or one number each from first and second rows , Therefore , the total number of ways is .
`""^(a)C_(2)+^(a)C_(1)xx^(a)C_(1)=(n(n-1))/(2)+n^(2)`
` =(3n^(2)-n)/(2)`