Question:

Find the number of $4$ letter words, with or without meaning, which can be formed out of the letters of the word , where the repetition of the letters is not allowed.

Updated On: Jul 6, 2022
  • $22$
  • $24$
  • $26$
  • $28$
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The Correct Option is B

Solution and Explanation

There are as many words as there are ways of filling in 4 vacant places
by the $4$ letters, keeping in mind that the repetition is not allowed. Thus, the number of ways in which the $4$ places can be filled, by the multiplication principle, is $4 \times 3 \times 2 \times 1 = 24$. Hence, the required number of words is $24$.
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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.