Question:

How many words can be formed from the letters of the word DOGMATIC, if all the vowels remain together :

Updated On: Jul 6, 2022
  • 4140
  • 4320
  • 432
  • 43
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The Correct Option is B

Solution and Explanation

Total numbers of letters in the given word = 8 Total no. of 8 letters word formed = P (8, 8) = 8! No. of vowels = 3 (i.e., O, A, I) If we consider these three vowels as one letter, then the number of different words = 8 - 3 = 5 + 1 (as 3?? vowels are considered as 1 word) Hence, the total number of 8 letters in which vowel remains together = P (3 $\times $ 3) $\times $ P (6 $\times $ 6) = 3! $\times $ 6! = 6 $\times $ 720 = 4320
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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.