How many 7 number combinations in 10 numbers?

Answer 1

Without repeating any of the numbers (each used once) = 120 unique "sets" of 7 numbers

(i.e. 1234567, 1234568, 1234569, 1234560, 1234578, 1234579, 1234570, 1234589, 1234580, 1234590)

If the order matters, you have a much larger number of combinations. (see below) Each of the 120 sets can be arranged in 5040 ways.

For a set of N numbers, the possible combinations using K numbers is N! / K! x (N-K)!

10! = 3,628,800

7! = 5040

(10-7)! = 3! = 6

The shortcut is (10 x 9 x 8) / (3 x 2) = 720/6 = 120

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For rearrangement of numbers (ordered sets), there are 604,800 possible numbers

N! / (N-K) ! = 10! / 3! = 3,628,800 / 6 = 604,800

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For unlimited repetition, there are 10,000,000 (1 x 10^7)