Question:

Given $4$ flags of different colours, how many different signals can be generated, if a signal requires the use of $2$ flags one below the other?

Updated On: Jul 6, 2022
  • $12$
  • $13$
  • $14$
  • $15$
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The Correct Option is A

Solution and Explanation

There will be as many signals as there are ways j of filling in $2$ vacant places $\boxminus$, in succession by the $4$ flags of different colours. Hence, by the multiplication j principle, the required number of signals $= 4 \times 3 = 12$.
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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.