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I.S.I. and C.M.I. Entrance

Sitting arrangement | ISI-B.stat | Objective Problem 120

Try this beautiful problem from TOMATO useful for ISI B.Stat Entrance based on Sitting Arrangement. You may use sequential hints.

Try this beautiful problem Based on Sitting Arrangement, useful for ISI B.Stat Entrance.

Sitting arrangement | ISI B.Stat Entrance | Problem 120


Three boys of class I, 4 boys of class II and 5 boys of class III sit
in a row. The number of ways they can sit, so that boys of the same
class sit together is

  • (a) \(3!4!5!\)
  • (b) \(12!/(3!4!5!)\)
  • (c) \((3!)^2 4!5! \)
  • (d) \(3*4!5!\)

Key Concepts


Probability

combinatorics

Permutation

Check the Answer


But try the problem first…

Answer: (c) \((3!)^2 4!5! \)

Source
Suggested Reading

TOMATO, Problem 120

Challenges and Thrills in Pre College Mathematics

Try with Hints


First hint

Let us take the boys of each class as an unit.Therefore there are 3 units which can be permutated in 3! ways.
Now, class I boys can permutate among themselves in 3! ways, class II boys
in 4! And class III boys in 5! ways.

Can you now finish the problem ……….

Final Step

Therefore, total number of ways is (3!3!4!*5!) = \((3!)^24!5!\)

Therefore option (c) is the correct

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