How many ways are there to select the $4$ subjects, and then decide the order of doing homework?

Question

Minnie has homework from 6 subjects including calculus and statistics this week. Among them, she wants to finish homework for 4 subjects including calculus and statistics today. She wants to finish statistics before calculus. How many ways are there for her to select the 4 subjects, and then decide the order of doing homework?

My Work: $\binom 42 = 6$ (Ways to select 2 subjects that are not Calc and Stat to make 4 subjects in total).

Then $P(4,4) = 24$ (Ways to order those four subjects). But then you divide by $4$ to get $6$ ways to order them to get stat before calc like the question asks.

So $6 \times 6 = 36$ ways in total. But other answers I see give $72$? What am I doing wrong?

Any Help/Tips would be appreciated. Thank You.

Answer 1

There are 6 ways to make statistics before calculus (i.e. 1-2, 2-3, 3-4, 1-3, 2-4, 1-4) and 2 ways to select the others two subjects then we obtain 12 ways to order the 4 subjects.

Answer 2

I think your workings are correct except for the final division by 4. Surely the divisor should be 2, as by symmetry in the total number of combinations there must be an equal number of cases where calculus precedes statistics,and vice versa.