Question

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?

Answer 1

Answer:

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