Question

how many arrangements are there of all the vowels adjacent in sociological?

Answer 1

Since there are 60 Xi, and for each of them there are 1260 distinct permutations of the letters in SOCIOLOGICAL, in which all the vowels are adjacent, totally in 60. 1260 =75600 of the arrangements of the letters in SOCIOLOGICAL, all the vowels are adjacent.

Answer 2

Answer:

there are 2016 arrangements of all the vowels adjacent in "sociological."

Explanation:

The question asks for the number of arrangements of all the vowels (i, o, and a) in the word "sociological" such that they are adjacent. To solve this problem, we can use the concept of permutations.

• A permutation is an arrangement of objects in a particular order. To find the number of permutations, we first need to determine the number of ways to arrange the vowels and then the number of ways to arrange the consonants around the vowels.

• In the word "sociological," there are 3 vowels (i, o, and a), and 5 consonants. To find the number of arrangements where all the vowels are adjacent, we first need to arrange the vowels in a block and then arrange the consonants around that block.

• There are 3! = 6 ways to arrange the vowels in the block, since there are 3 different vowels. Then, there are (5+3)! / (5! * 3!) ways to arrange the vowels and consonants, since there are a total of 5+3=8 letters in the word "sociological."

Finally, the number of arrangements with all the vowels adjacent is simply the product of these two arrangements: 6 * (8! / (5! * 3!)) = 6 * (40320 / (120 * 6)) = 6 * 336 = 2016.

Therefore, there are 2016 arrangements of all the vowels adjacent in "sociological."

To learn more about permutations from the link below

https://brainly.in/question/653775

To learn more about  vowels  from the link below

https://brainly.in/question/15049851

#SPJ3