Question

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

Answer 1

Answer:

48 ways

Step-by-step explanation:

Given

$Girls = \{Ava, Cara, Emma, Lily, Mia\}$

$Together= \{Emma, Lily\}$

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:

$Ways = 2! * (5 - 1)!$

$Ways = 2! * 4!$

$Ways = 2 * 1 * 4 * 3 *2 * 1$

$Ways = 48$

Hence, there are 48 ways

Answer 2

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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