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In how may ways can the letters of the word 'SEMESTER' be arranged such that at least two vowels are together. Show ALL your work step by step to get credit. Final answers MUST be provided in decimal form



Answer :

varshamittal029

In 720 ways the letters of the word 'SEMESTER' be arranged such that at least two vowels are together.

Arrangement in probability

  • A number of topics like statistics and probability are closely interrelated to the topic of permutation and combination.
  • Permutation and combination is about making arrangements and making selections on the basic of certain formulas.

Given that:

In SEMESTER there are 8 letters.

Which include 3 vowels (E) and 5 consonants (S, M, T , R )

Take 3 vowels as one letter, we have 6 letters

arranged in 6[tex]p_{6}[/tex] = 6! ways E can be taken together in 1! ways

Number of words = 6! × 1!

                             = 6 × 5 × 4 × 3 × 2 × 1

                             = 720 ways

To learn more about vowels and consonants check the given link

https://brainly.com/question/27999334

#SPJ4

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