+0  
 
0
613
8
avatar+36 

1)  In how many ways can I arrange 3 different math books and 5 different history books on my bookshelf, if I require there to be a math book on both ends?

 

2)  I have 10 distinguishable socks in my drawer: 4 white, 4 brown, and 2 blue. In how many ways can I choose a pair of socks, provided that I get two socks of different colors?

 

 

tytyty! c:

Echotastic  Feb 17, 2018
 #1
avatar
0

Dont post problems from AOPS, its not worth it

Guest Feb 17, 2018
 #3
avatar+13644 
0

Your keyboard seems to have a problem with the apostrophe key.

ElectricPavlov  Feb 18, 2018
 #2
avatar+13644 
+1

I think:

1.

There are 6 different ways a math book can be at both ends.

That leaves 6 books in the middle that can be arranged 6! ways

6 x 6! = 4320

ElectricPavlov  Feb 18, 2018
 #4
avatar+91213 
+1

1)  In how many ways can I arrange 3 different math books and 5 different history books on my bookshelf, if I require there to be a math book on both ends?

 

We have   P(3,2)  =  6 ways to arrange the math books  and 6! ways of arranging the 1 math book and 5 history books in the middle....  so...6 x 6!  =   6 x 720  =  4320 ways

 

 

2)  I have 10 distinguishable socks in my drawer: 4 white, 4 brown, and 2 blue. In how many ways can I choose a pair of socks, provided that I get two socks of different colors?

 

We  can  either have   

White - Brown  =  4C1 x 4C1  =  4 x 4  =  16 ways

Brown - Blue  =  4C1 x 2C1   =   4 x 2   = 8  ways

White -Blue  = 4C1  x 2C1  =   4 x 2  =  8 ways

 

So...the total ways =   16 + 8 + 8  =   32

 

  ( EDIT )

 

cool cool cool

CPhill  Feb 18, 2018
edited by CPhill  Feb 18, 2018
 #5
avatar+13644 
0

Hey CPhil....   What about the other math book?  5 history books + 1 math book = 6 books in the middle.

ElectricPavlov  Feb 18, 2018
 #6
avatar+91213 
0

You are correct, EP!!!!...I'll edit my answer  !!!

 

 

 

cool cool cool

CPhill  Feb 18, 2018
 #7
avatar+36 
0

Hi, I don't understand how you got the p(3,2) can you explain it to me? (Thank you! I'm really struggling with this topic.)

Echotastic  Feb 18, 2018
 #8
avatar+91213 
0

P (3,2)   means that  we are choosing any 2 things out of 3 and then permuting (giving all the possible orders  of the things selected )

 

So...suppose the math books  are  A, B and C

 

The possible selections we can make is   

 

{ A, B}   { B , C}  or { A, C}    (1)

 

But  we can also arrange these as  { B, A}  {C, B}  or   {C, A}.......so we have a total of 6 possible arrangements

 

Note that   (1)  is  C(3,2) = 3  =   the number of possible sets

 

But  P(3,2)   =  6  =  the number of posssible arrangements of these sets

 

[ This stuff is hard for everyone  !!!  ]

 

 

cool cool cool

CPhill  Feb 18, 2018

24 Online Users

avatar
avatar
avatar

New Privacy Policy

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive information about your use of our website.
For more information: our cookie policy and privacy policy.