Ava, Cara, Emma, Lily, and Mia are to be seated together in a row. If Emma and Lily must sit next to each other, how many different ways can the five girls be seated

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.

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48 ways

Step-by-step explanation:

Given

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:

Hence, there are 48 ways

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