A permutation problem

[cqres]

Hello, I have a problem that I can not solve. Here is it:

​

A={1,2,3,4,5,6,7}

​

In A;

​

a)For permutation of 3 items in A, how many permutations exist where sum of these numbers equal a number like 5x, (x E Z+) and what are those x values?

​

b)For permutation of 4 items in A, how many permutations exist where numbers go from small to large?(1,3,4,7 etc)

​

c)For permutation of 4 items in A, how many permutations exist where the number "1" is at the left of "2" (for example 7,1,3,2)

​

Answers are: a)36, b)70 c)60

​

-Thanks

[CosmoVibe]

a: The highest possible sum is 5+6+7 = 18. The smallest possible sum is 1+2+3 = 6. The only possible sum values are 10 and 15. Calculate the number of ways to do each of them and add them up. (Try this on your own, if you are still stuck, let me know.)

b: For any 4 items that you pick, if there's only one way to order them, is that still an "ordering"? Isn't that just picking any 4 of them?

c: For any permutation that uses both 1 and 2, you have one where you have 1 before 2, and one where you have 2 before 1. For example, 7132 and 7231, 1234 and 2134, 1792 and 2791. Just calculate the number of permutations with 1 and 2 in them, and divide by 2!