Final answer:
To solve this problem, we need to use a permutation, as the order of the girls matters. There are 6 ways the girls can fill the roles of a grandmother, mother, and daughter.
Step-by-step explanation:
To solve this problem, we need to determine whether a permutation or combination should be used. In this case, we are interested in how many ways the girls can fill the roles of a grandmother, mother, and daughter, which implies that the order of the girls does matter. Therefore, we should use a permutation.
To calculate the number of permutations, we can use the formula for permutations of n objects taken r at a time, which is nPr = n! / (n-r)!, where n is the total number of objects and r is the number of objects being selected. In this case, n = 3 (number of girls) and r = 3 (number of roles to be filled). Plugging these values into the formula, we get 3P3 = 3! / (3-3)! = 3! / 0! = 6.
Therefore, there are 6 ways the girls can fill the roles of a grandmother, mother, and daughter.