Probability of 2 items not next to each other

[desmond iking]

Homework Statement

i am having problem on part e , the ans given is 504-(7c1 X4 )= 476

but my working would be 504-(7c1 X4 x2 )= 448

since the pure maths and statistics can be arranged in 2! ways , but the 1 tem which is chosen from 7 items can be placed in 4 location , just as in the picture.

Homework Equations

The Attempt at a Solution

 

[HallsofIvy]

I have no idea what you mean by "but the 1 tem which is chosen from 7 items can be placed in 4 locations". (c) and so (e) refer to choosing 3 items out of 9. There are NO "4 locations".
How many different ways are there to choose 3 items out of 9 and then place them in some order? (i.e. part (c)). How many of those involve choosing the pure math and statistics text. How many of those have the two texts as first and second or as second and third? Subtract the second answer from the first.

 

[D H]

The answer in the book is correct.

Your "4x2" doesn't make sense. Consider three items, labeled A, B, and C, and arranged in a line. Some of the arrangements have items A and B adjacent, others don't. The total number of arrangements is 3!=6. The number in which items A and B are adjacent has to be less than this.