Q50 / 125 · BITSAT 2014 · Mathematics

The number of all three elements subsets of the set $\left\{a_{1}, a_{2}, a_{3} \ldots a_{n}\right\}$ which contain $a_{3}$ is

  • A
    ${ }^{\mathrm{n}} \mathrm{C}_{3}$
  • B
    ${ }^{\mathrm{n}-1} \mathrm{C}_{3}$
  • Correct answer
    C
    ${ }^{\mathrm{n}-1} \mathrm{C}_{2}$
  • D
    None of these

Solution

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

Hence, the correct answer is option: 'C'.

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