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NDA 1 2025 Maths, question 29

Topic: Algebra

Q29

What is the number of selections of at most 3 things from 6 different things?

  1. (a) 20
  2. (b) 22
  3. (c) 41Correct answer
  4. (d) 42

Solution.

Answer: (c) 41

  1. Selecting at most 3 things means selecting 1, 2 or 3 of them.
  2. (61)+(62)+(63)=6+15+20=41\binom{6}{1} + \binom{6}{2} + \binom{6}{3} = 6 + 15 + 20 = 41.

Trap: Counting the empty selection too gives 41+1=4241 + 1 = 42, option (d); a selection normally means choosing at least one thing.