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

885

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1335

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1770

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3670

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Solution

The correct option is B 1335
Given numbers can be arranged as
$1, 4, 7, . . . .88 \to 30 n u m b e r s 2, 5, 8, . . . .89 \to 30 n u m b e r s 3, 6, 9, . . . .90 \to 30 n u m b e r s$
Total ways $=^{30} C_{2} +^{30} C_{1} .^{30} C_{1} = 435 + 900 = 1335$

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