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Sagot :
Answer:
48 ways
Step-by-step explanation:
Given
[tex]Girls = \{Ava, Cara, Emma, Lily, Mia\}[/tex]
[tex]Together= \{Emma, Lily\}[/tex]
Required
Determine the number of sitting arrangements
The number of girls are 5, of which 2 must be seated together.
First, Emma and Lily can be arranged in 2! ways
Next, we consider Emma and Lily as one, so there are (5 - 1) girls left to be arranged.
This can be done in (5 - 1)! ways
Total number of ways is then calculated as:
[tex]Ways = 2! * (5 - 1)![/tex]
[tex]Ways = 2! * 4![/tex]
[tex]Ways = 2 * 1 * 4 * 3 *2 * 1[/tex]
[tex]Ways = 48[/tex]
Hence, there are 48 ways
The possible ways in which Ava, Cara, Emma, Lily, and Mia are to be seated together in a row, while Emma and Lily sit next to each other are 48 ways.
Given to us;
Number of girls = {Ava, Cara, Emma, Lily, and Mia} = 5 girls,
Also, Emma and Lily must sit next to each other, therefore, considering them as a single person,
The choices we are left with = {Ava, Cara, Mia, (Emma, Lily)} = 4 person;
We know to calculate the number of ways people can sit is given by n! (n factorial), where n is the number of person. Thus,
different ways this 4 person can sit = n!
= 4!
= 4 x 3 x 2 x 1
= 24 ways
Further, as given in the question Emma and Lilly must sit together but they can change sits within themselves, So,
different ways Emma and Lilly can sit = n!
= 2!
= 2 x 1
= 2 ways
Therefore, the total number of ways all 5 girls can sit together in which Emma and Lilly will be always seated together,
Total ways all can sit together = 24 x 2
= 48 ways
Hence, the possible ways in which Ava, Cara, Emma, Lily, and Mia are to be seated together in a row, while Emma and Lily sit next to each other are 48 ways.
To know more visit:
https://brainly.com/question/13003667
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