Math 3C Supp problems 1.pdf

# Second approach a multistep process in the first step

• DarkThunderKnight27
• 3

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Second approach: A multistep process. In the first step, we choose 3 out of the 10 positions to be green. In the second step, we choose 2 of the remaining 7 positions to be red. In the final step, we pick an arrangement of the 5 remaining balls in the 5 remaining positions. There are 10 3 7 2 5! = 10! 7!3! 7! 5!2! 5! = 10! 3!2! possible orderings. Third approach: A different multistep process. We first place the 5 miscel- laneous balls into 5 of the 10 positions in some order ( P (10 , 5) options). In the second step, we choose 3 of the 5 remaining positions to receive green balls ( ( 5 3 ) options). There are 2 positions left, and they will both receive red balls ( ( 2 2 ) options). There are P (10 , 5) 5 3 2 2 = 10! 5! 5! 3!2! · 1 = 10! 3!2! possible orderings. A question to see if you have the idea: 2

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Question 5. A track and field team is attending a competition. There are 8 team members (all distinguishable!) and 14 events. The two team captains will participate in two events each, the other six will only participate in one each. (The team will skip four events.) How many possible arrangements are there? 3
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• Summer '14
• N/A
• Math, Probability, BR postcode area, Color blindness, possible orderings

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