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I have 5 different pullover shirts and 4 different button-down shirts. In how many ways can I choose shirts for the next 9 days if I insist on wearing pullover shirts two days in a row at least once? Assume that I wear one shirt each day, and every shirt gets worn once.

Guest Jun 4, 2017
 #1
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I have 5 different pullover shirts and 4 different button-down shirts. In how many ways can I choose shirts for the next 9 days if I insist on wearing pullover shirts two days in a row at least once? Assume that I wear one shirt each day, and every shirt gets worn once.

 

There are 9! ways with no restrictions and

 

If 2 pullover shirts are NOT worn two days in a row then it will be

P B P B P B P B P      

 

So the pullovers will have to be in the 1st 3rd 5th 7th and 9th positions  

these can be arranged in 5! ways

 

The button shirts can be arranged  4! ways

so that is   5!*4! ways thate two button up will not be together

 

So the number of ways that at least 2 pullovers are worn on consecuative days is

 

9!  -  5!*4!

 

9!-5!*4! = 360000

Melody  Jun 4, 2017

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