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Question: question 7 consider 10 male students m m2 mi0 and...

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Question 7: Consider 10 male students M, M2,..., Mi0 and 7 female students Fi, F2,.... Fr. Assume these 17 students are arranged on a horizontal line such that no two female students are standing next to each other. We are interested in the number of such arrangements, where the order of the students matters. Explain what is wrong with the following argument We are going to use the Product Rule: ·Task 1: Arrange the 7 females on a line. There are ways to do this. ·Task 2: Choose 6 males. There are ways to do this . Task 3: Place the 6 males chosen in Task 2 in the 6 gaps between the females. There are 6! ways to do this. . Task 4: At this moment, we have arranged 13 students on a line. We are left with 4 males that have to be placed. Task 4.1: Place one male. There are 14 ways to do this. Task 4.2: Place one male. There are 15 ways Task 4.3: Place one male. There are 16 ways to do this. Task 4.4: Place one male. There are 17 ways to do this. By the Product Rule, the total number of ways to arrange the 17 students is equal to 7! 6! 14-15 - 16- 17-43, 528, 181, 760, 000.

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