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  • There are 5 consonants (B, C, D, F, G) and 4 vowels (A, E, I, O). In how many ways can the letters be arranged such that all the consonants and vowels alternate?  <div

There are 5 consonants (B, C, D, F, G) and 4 vowels (A, E, I, O). In how many ways can the letters be arranged such that all the consonants and vowels alternate?

 

Option: 1

15360


Option: 2

20360


Option: 3

17280

 


Option: 4

18820


Answers (1)

best_answer

To find the number of ways the 5 consonants (B, C, D, F, G) and 4 vowels (A, E, I, O) can be arranged such that all the consonants and vowels alternate, we can consider them as two separate groups.

First, let's arrange the consonants among themselves. Since there are 5 consonants, we can arrange them in 5! (5 factorial) ways.

Next, let's arrange the vowels among themselves. Since there are 4 vowels, we can arrange them in 4! ways.

Since we want the consonants and vowels to alternate, we can consider the positions in which the consonants will be placed. There are 6 possible positions for the consonants.

We need to choose 5 out of these 6 positions to place the consonants. 

Once we have chosen the positions for the consonants, the vowels will automatically fill the remaining positions.

Therefore, the total number of ways to arrange the letters such that the consonants and vowels alternate is:

5 ! \times 4 ! \times 6=17280

So, there are 17280 different ways to arrange the letters B, C, D, F, G, A, E, I, and O such that all the consonants and vowels alternate.

 

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