I have 7 different geography textbooks and 4 different chemistry textbooks. In how many ways can I line the 11 textbooks on a bookshelf if a chemistry textbook must be in the middle and there must be a geography textbook at each end?

Guest Dec 15, 2019

#1**+2 **

I'm not great at these counting problems, but here is my best attempt

We have 4 ways to choose the chemistry book that goes in the middle

And we have 7 ways to choose the geography book that goes first and 6 ways to choose the other geography book that goes last

And we have (3 + 5) = 8! ways to arrange the other books

So....the total arrangements = 4 * 7 * 6 * 8! = 6,773,760 arrangements

CPhill Dec 15, 2019

#2**+1 **

I have 7 different geography textbooks and 4 different chemistry textbooks. In how many ways can I line the 11 textbooks on a bookshelf if a chemistry textbook must be in the middle and there must be a geography textbook at each end?

G ?? C ?? G 4chem and 7geog

7*6*4* ..... So no I have 8 books left that can go anyremaing place

7*6*4*8! = 6773760 Our answers should be the same Chris. I used the web2 calc, I think it was imputed correctly.

Melody Dec 15, 2019

#4**-1 **

Melody, thank you for the correct answer!

CPhill, you could learn a thing or two from Melody about getting the right answer!

Guest Dec 15, 2019

#6**+3 **

You could learn a thing or 2 about manners guest!

CPhil's answer was spot on. A typo at the end is absolutely nothing.

You should be assamed of yourself talking to CPhill like that after he went out of his way to answer YOUR question!

Melody
Dec 15, 2019

edited by
Guest
Dec 15, 2019