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Matilda, Tanya and Renee are auditioning for a play. In how many ways can the girls fill the roles of a grandmother, mother, and daughter?


Would a permutation or combination be used to solve this problem?

Verified Answer :

JeanaShupp

Answer: 1) In 6 ways the girls can fill the roles of a grandmother, mother, and daughter.

2) A permutation would be used to solve this problem

Step-by-step explanation:

Permutation is an arrangement of the elements of a list into a one to one correspondence with itself, where as a combination is a collection of things in which order doesn't matter at all.

In the given situation there are three girls named Matilda, Tanya and Renee are auditioning for a play. The girls have to fill the roles of a grandmother, mother, and daughter that means no girl can take two roles or no two girls can 1 role i.e. repetition is not allowed so by permutation ,

the number of ways the girls can fill the roles=\(\frac{n!}{(n-r)!}=\frac{3!}{(3-3)!}=3!=6\),where n is the total roles and r is the number of girls.

Therefore, in 6 ways the girls can fill the roles of a grandmother, mother, and daughter.

Using arrangements, it is found that the girls can fill the roles in 6 ways.

In this question, we have 3 people for 3 roles, that is, the same number of people and roles, thus, the arrangements formula is used.

The number of possible arrangements of n elements is the factorial of n, that is:

\(A_{n} = n!\)

In this problem, 3 people for 3 roles, thus \(n = 3\), and:

\(A_{3} = 3! = 6\)

The girls can fill the roles in 6 ways.

A similar problem is given at https://brainly.com/question/24648661

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