Question

Total number of ways of selecting two numbers from the set {1,2,3,.....,90} so that their sum is divisible by 3, is

• A. $885$
• B. $1335$
• C. $1770$
• D. $3670$

Answer 1

The correct option is B $1335$

No of multiples of 3 in $\{1,2,3,...90\}=30$

No of numbers which give '1' remainder in $\{1,\mathrm{2...90}\}=30$

No of number which give '2; remainder in $\{1,\mathrm{2...90}\}=30$

case : selecting '2' numbers which are divisible by $3$

$30c_2=\frac{30\times 29}{2}=435$

case: selecting '2' number where are gives

remainder '1' other remainder $2$

$30c_1\times 30c_1=900$

Total ways (pairs) $=900+435=1335$