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BITSAT 2014
Exam
BITSAT
Year
2014
Subject
Mathematics
Chapter
Permutation and Combination

BITSAT 2014 · Mathematics · Permutation and Combination

The number of all three elements subsets of the set \ a_ 1 , a_ 2 ,...

The number of all three elements subsets of the set {a1,a2,a3…an}\left\{a_{1}, a_{2}, a_{3} \ldots a_{n}\right\} which contain a3a_{3} is

Options

  1. AnC3{ }^{\mathrm{n}} \mathrm{C}_{3}
  2. Bn−1C3{ }^{\mathrm{n}-1} \mathrm{C}_{3}
  3. Cn−1C2{ }^{\mathrm{n}-1} \mathrm{C}_{2}
  4. DNone of these

Correct answer

C. n−1C2{ }^{\mathrm{n}-1} \mathrm{C}_{2}

Step-by-step solution

The number of three elements subsets containing a3\mathrm{a}_{3} is equal to the number of ways of selecting 2 elements out of n−1\mathrm{n}-1 elements. So, the required number of subsets is n−1C2{ }^{\mathrm{n}-1} \mathrm{C}_{2}
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