How many combinations of 6 numbers are there in 16 numbers What are these combinations?

Answer 1

There are 16C6 combinations = 16!/(6!(16-6)!) = 16!/(6!10!) = 8,008 possible combinations.

Assuming the 16 numbers are the hexadecimal digits 0-F, they are:

{0, 1, 2, 3, 4, 5}, {0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 4, 7}, ...., {0, 1, 2, 3, 4, E}, {0, 1, 2, 3, 4, F},

{0, 1, 2, 3, 5, 6}, ..., {0, 1, 2, 3, 5, F},

{0, 1, 2, 3, 6, 7}, ...., {0, 1, 2, 3, 6, F}, ...., {0, B, C, D, E, F}, {1, 2, 3, 4, 5}, ...,

{9, A, B, C, D, E}, {9, A, B, C, D, F}, {9, A, B, C, E, F}, {9, A, B, D, E, F},

{9, A, C, D, E, F}, {9, B, C, D, E, F}, {A, B, C, D, E, F}

I'll let you fill in the missing 7,990 possible combinations.

Answer 2

There are 8008 of them and you must think me crazy if you think I have got time to list them all!