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?

120960

Step-by-step explanation:

We get 11 books 7 of geography and 4 of chemistry

We need to line all of them with 2 constraints

1.-three of the geography must be: 1 in the middle and in each end, then we already have

C₄,₃ = 4! / (4 - 3) ! C₄,₃ = 4*3*2*1

C₄,₃ = 24 different ways

Now we have 7 books of chemistry. To place them we get

P₇ = 7! P₇ = 7*6*5*4*3*2*1 P₇ = 5040

Now the total number will be

C₄,₃ * P₇ = 120960