How many ways are there to make a schedule of 6 subjects There are 6 different subjects including maths and physics.
How many ways are there to make a schedule of 6 subjects such that physics follows maths?
Actually I tried to denote maths as M and physics as P.
Then I started to count like this.
MXXXXX - number of ways  - 5!
XMXXXX - number of ways  - 4*1*4*3*2*1 = 96
XXMXXX - number of ways  - 4*3*1*3*2*1 = 72
XXXMXX - number of ways  - 4*3*2*1*2*1 = 48
XXXXMX - number of ways  - 4*3*2*1*1*1 = 24
And then sum them up, getting 360, but actually the correct answer to the problem is 240.
Can anyone help me solve this problem?
 A: Your answer is correct.
There are six slots to fill.  We can fill two of those six slots with mathematics and physics in $\binom{6}{2}$ ways.  Since physics must follow maths, there is only one way to arrange mathematics and physics in those slots.  For each of these ways of scheduling maths and physics, there are $4!$ ways of arranging the other subjects in the four remaining slots.  Hence, the number of possible schedules in which physics follows mathematics is 
$$\binom{6}{2} \cdot 4! = 360$$
as you found.
A: Your answer is correct. Another method leading to the same result:
$$\binom62\times4!=15\times24=360$$
From $6$ spots first select $2$ for maths and physics. Then place the other subjects in some order. There are $4!$ orders.
A: There are 6! = 720 ways to order the six subjects.  Half these orderings will have math before physics.
A: Choose 2 slots for m and p: $\binom{6}{2}$, this accounts for the fact that p follos m. For each such choice you have 4! allocations of other subjects
A: The total number of ways for arranging those $6$ subjects is $6!=720$.
Physics may equally likely appear before Math and after Math.
So there are $720/2=360$ arrangements with Physics after Math.
A: The correct answer is 240 because:
Imagine the math and physics classes together as a "package", they can be thought of as one two hour long class following each other. Considering that, there will be 5!=120 different schedules. However, within the "physics-math class", you can take physics first or math first, so there are 2!=2 ways to do that. Therefore, the total possible schedules are:
       5!2!=240 schedules possible

We solved a very similar problem in precalculus recently 
