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Permutations with subject groups

CMAT 2020 · Quantitative Techniques & Data Interpretation · Medium · Permutation and Combination

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There are six teachers. Out of them, two teach physics, other two teach Chemistry and the rest two teach Mathematics. They have to stand in a row such that Physics, Chemistry and Mathematics teachers are always in a set. The number of ways in which they can do, is :

  1. A.

    24

  2. B.

    48

  3. C.

    36

  4. D.

    12

Answer

B

Explanation

There are 3 sets of subject teachers (Physics, Chemistry, Math). The 3 sets can be arranged among themselves in 3!=63! = 6 ways. Within each set, the 2 teachers can be arranged in 2!=22! = 2 ways.

Total ways = 3!×2!×2!×2!=6×8=483! \times 2! \times 2! \times 2! = 6 \times 8 = 48.

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