Question:

Four students of class X, five students of class XI and six students of class XII sit in a row. The number of ways, they can sit in a row so that students belonging to the same class are together is :

Updated On: Jul 6, 2022
  • 3! 4! 5! 6!
  • 3 $\times$ 4! 5! 6!
  • 4! 5! 6!
  • $\frac{15!}{4! 5! 6!}$
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The Correct Option is A

Solution and Explanation

Treating them as three groups, the three groups can be arranged in 3! ways. There after each group can be arranged internally. Total number = 3! $\times$ 4! $\times$ 5! $\times$ 6!
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Notes on permutations and combinations

Concepts Used:

Permutations and Combinations

Permutation:

Permutation is the method or the act of arranging members of a set into an order or a sequence. 

  • In the process of rearranging the numbers, subsets of sets are created to determine all possible arrangement sequences of a single data point. 
  • A permutation is used in many events of daily life. It is used for a list of data where the data order matters.

Combination:

Combination is the method of forming subsets by selecting data from a larger set in a way that the selection order does not matter.

  • Combination refers to the combination of about n things taken k at a time without any repetition.
  • The combination is used for a group of data where the order of data does not matter.