Question

find the number of 8-digit numbers abcdefgh with distinct digits from 1 to 8 such that a > b > c > d and d < e < f < g < h.

Answer 1

Answer: 70

Explanation:

Note that we can find the number of ways to choose 4 numbers out of the 8 to represent the unordered triple
`(a,b,c,d)`. The other 4 numbers will represent the unordered triple
`(e,f,g,h)`. For each of these triples, there is only one allowed permutation because the numbers need to be in sequential order.

So, the final answer is
`\binom{8}{4}=70`.