How many combinations of 6 numbers in ascending order can you make from 1 - 52?

Answer 1

I suggest you use an heuristic approach by setting yourself a computationally smaller problem, namely, how many combinations of 3 numbers in ascending order can be made from the digits 0 through 5?

This is 'computationally smaller' in the sense that one can write down all of the combinations in a couple of minutes.

(0, 1, 2)

(0, 1, 3)

(0, 1, 4)

(0, 1, 5)

(0, 2, 3)

(0, 2, 4)

(0, 2, 5)

(0, 3, 4)

(0, 3, 5)

(0, 4, 5)

(1, 2, 3)

(1, 2, 4)

(1, 2, 5)

(1, 3, 4)

(1, 3, 5)

(1, 4, 5)

(2, 3, 4)

(2, 3, 5)

(2, 4, 5)

(3, 4, 5)

Not only that, when I write them down in this way I see that, in writing them systematically (to ensure that I have them all) I notice that they are in ascending order! So this question is equivalent to asking how many ways there are of choosing 3 items from 6 (without any conditions).

Going back to the original question I now know that one need not write out all of the combinations, I can simply calculate the number of ways of choosing 6 items from 52, which is 20358520.