Matilda, Tanya and Renee are auditioning for a play. In how many ways can the girls fill the roles of a grandmother, mother, and
2 answers:
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=,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.
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Answer:
Step-by-step explanation:
refers to the permutations of 5 items taken 3 at a time. To evaluate this, we use factorials as follows;
The factorial of an integer n is evaluated as;
Using this concept, the above expression can now be simplified as follows;
Therefore, the permutations of 5 items taken 3 at a time is 60.
The next expression, refers to the combinations of 6 items taken 4 at a time. The simplification utilizes similar concepts of permutations since we shall be involving factorials;
Therefore, the combinations of 6 items taken 4 at a time is 15.
The final step is to evaluate the product;