NDA 2023 Maths · Mathematics · Permutations and Combinations · hard

The number of ways of selecting 3 distinct numbers from \1,2,…,20\ such that their sum is divisible by 3 is

Single correct option

The number of ways of selecting

3

distinct numbers from

\{1,2,\dots,20\}

such that their sum is divisible by

3

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Answer: (C) $384$

Among

1

20

there are

6

numbers with remainder

0

, and

7

each with remainders

1

and

2

. The sum is divisible by

3

if all three share a remainder or the remainders are

0,1,2

\binom63+\binom73+\binom73+6\cdot7\cdot7=20+35+35+294=384

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