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1.My school's math club has 6 boys and 8 girls. I need to select a team to send to the state math competition. We want 6 people on the team. In how many ways can I select the team without restrictions?

 

 

2.Twenty switches in an office computer network are to be connected so that each switch has a direct connection to exactly three other switches. How many connections will be necessary?

Guest Mar 10, 2018
 #1
avatar+91443 
+1

Don't know the second one.....but for the first

 

We want to choose  any 6 people from 14....so

 

C(14,6)   = 3003  ways 

 

 

cool cool cool

CPhill  Mar 10, 2018
 #2
avatar
0

but can you explain why (14,6) = 3003 im really confused on why that equals 3003

Guest Mar 10, 2018
 #3
avatar+91443 
+1

C (n, m)  is defined as

 

       n!

__________

(n - m)! * m!

 

So

 

C(14,6)  =

 

      14!                       14!             14*13*12*11*10*9

___________  =     ______  =    _______________  =

  (14 - 6)! * 6!           8! * 6!                   6!

 

 

2162160

_______    =     3003

   720

 

 

cool cool cool

CPhill  Mar 10, 2018
 #4
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0

what would c=(223,221) be?

Guest Mar 10, 2018
 #5
avatar+91443 
+1

C (223, 221)  =

 

    223!                             223 * 222         223 * 111  = 24753

_______________  =      ________  =

(223 - 221)! * 221!                2! 

 

 

 

cool cool cool

CPhill  Mar 10, 2018

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