Answer:
Step-by-step explanation:
This is one minus the probability that all the girls audition for different roles. The total number of ways of assigning roles to the girls is 12^7, because to each of the 7 girls, you have a choice of 12 roles.
Then if each girl is to receive a different role, then there are 12!/5! possibilities for that. If you start assigning roles to the girls, then for the first girl, there are 12 choices, but for the next you have to choose one of the 11 different ones, so 11 for the next, and then one of the 10 remaining for the next etc. etc., and this is 12*11*10*...*6 = 12!/(12-7)! =12!/5!
The probability that a random assignment of one of the 12^7 roles would happen to be one of the 12!/5! roles where each girl has a different role, is
(12!/5!)/12^7 = 12!/(12^7 5!)
Then the probability that two or more girls addition for the same part is the probability that not all the girls are assigned different roles, this is thus:
1 - 12!/(12^7 5!)
Answer:
C
Step-by-step explanation:
The sample used in this problem is classified as cluster.
<h3>How are samples classified?</h3>
Samples may be classified as:
- Convenient: Drawn from a conveniently available pool.
- Random: All the options into a hat and drawn some of them.
- Systematic: Every kth element is taken.
- Cluster: Divides population into groups, called clusters, and each element in the cluster is surveyed.
- Stratified: Also divides the population into groups. Then, a equal proportion of each group is surveyed.
For this problem, a group of schools is selected, and then the new program is applied to all students in these school, meaning that all elements in the cluster are surveyed, so cluster sampling is used.
More can be learned about classification of samples at brainly.com/question/25122507
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