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A group of 10 representatives is to be selected out of 12 seniors and 10 juniors. In how many different ways can the group be selected, if it should have 5 seniors and 5 juniors?

Correct answer: C. ¹²C₇ * ¹⁰C₅

  • A. ¹²C₅ * 10
  • B. ¹²C₇ * 10
  • C. ¹²C₇ * ¹⁰C₅
  • D. 12 * ¹⁰C₅

Explanation

The 5 seniors can be selected in ¹²C₅ ways, and independently the 5 juniors can be selected in ¹⁰C₅ ways. By the multiplication principle, the total is ¹²C₅ x ¹⁰C₅. The likely trap is ¹²C₇ x ¹⁰C₅, which selects 7 seniors rather than the required 5.

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