The questions are as follows:
On a shelf there are 4 different mathematics books and 8 different English books.
i) The books are to be arranged so that the mathematics books are together. In how many different ways can this be done?
Answer: 4!*9! = 8 709 120
I did not have any problem with the question and answer above, but the problem is the next one:
ii) What is the probability that all the mathematics books are NOT together.
I would interpret it as the complement of "all the mathematics books are together", so my working would be, using the result of i) above,
1 -
On a shelf there are 4 different mathematics books and 8 different English books.
i) The books are to be arranged so that the mathematics books are together. In how many different ways can this be done?
Answer: 4!*9! = 8 709 120
I did not have any problem with the question and answer above, but the problem is the next one:
ii) What is the probability that all the mathematics books are NOT together.
I would interpret it as the complement of "all the mathematics books are together", so my working would be, using the result of i) above,
1 -
8 709 120/12! = 54/55
However, the textbook says that the correct answer is 9/30.
Please tell me what's wrong with my working and why the answer is 9/30.
Also, even if we interpret the question as "none of the mathematics books are next to each other", a correct working would be:
(9P4)*8!/12! = 14/55, which is still different to the answer provided in the textbook.
I would much appereciate it if someone can help me to see what's wrong with my working.
Thank you.
However, the textbook says that the correct answer is 9/30.
Please tell me what's wrong with my working and why the answer is 9/30.
Also, even if we interpret the question as "none of the mathematics books are next to each other", a correct working would be:
(9P4)*8!/12! = 14/55, which is still different to the answer provided in the textbook.
I would much appereciate it if someone can help me to see what's wrong with my working.
Thank you.