What are the 4 number combinations out of 8 numbers?

Answer 1

This is an ambiguous question. Are you asking for the number of combinations, or to actually list them? Since we haven't been given the 8 numbers, I assume the former. Are you asking for the number of combinations of 4 different numbers selected from the given 8, or are duplicates allowed?

The latter is kind of complicated. The number of permutations of 4 numbers selected from 8 given numbers (or any 8 things) is very easy: since each of the 4 positions in the sequence can be any of the 8, you get 8 raised to the 4th power, which is 4096. But to get the number of combinations, you have to eliminate the duplications, and the number of duplications for a permutation depends on the number of repetitions within the permutation itself. For example, the permutation (1, 2, 1, 2) has 2 pairs; you need to count the number of combinations of the 4 positions where the 1s can go, and the other 2 positions would have 2s. That number turns out to be 6, but if there is only 1 pair, as in (1, 1, 2, 3) you have 6 pairs of positions to put the 1s in, and 2 ways of ordering the 2 and the 3, so you get 12. I could go on and on.

If you don't allow duplications, then you have 8 x 7 x 6 x 5 possible permutations, which is 1,680. Each of these can be ordered 4 x 3 x 2 x 1 ways, which is 24. Dividing 1,680 by 24 gives 70 combinations