americasmiller
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The letters of the word COMBINE are placed at random in a row. In how many ways can an arrangement occur such that all vowels are placed together? Show all of your work for full credit.

(This is a permutation math problem)

Respuesta :

mmkmarcial

I think its 210 because there are 7 letters and 3 vowels so the permutation would be 7 P 3.

There are 35 ways through which an arrangement occur such that all vowels are placed together in the word COMBINE.

What are combinations?

A combination is a calculation that determines the number of possible arrangements in a collection of items in which the order of the selection does not matter. In combinations we can select the items in any order.

n[tex]C_{r}=[/tex]n!/r!(n-r)!

How to calculate number of ways?

We have been given word "COMBINE".

Number of vowels in the word=3

Total alphabets in the word=7

Number of ways=7[tex]C_{3}[/tex]

=7!/3!(7-3)!

=7!/3!4!

=7*6*5*4!/3!4!

=7*6*5/3*2*1

=35 ways

Hence there are 35 ways through which arrangement can occur such that all vowels are placed together in the word COMBINE.

Learn more about combinations at https://brainly.com/question/11732255

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