In how many ways can you arrange seven items, taking only 3 at a time?

To arrange 7 items, taking only 3 at a time and assuming that the order of those 3 items do not matter, the procedure is as below:

You first pick 3 items out of 7 original items (combination with n = 7 and k = 3), then you pick 3 items out of 4 remaining items (combination with n = 4 and k = 3), the last item is automatically chosen.

=> Number of ways to do this:

N = 7C3 x 4C3

   = 7!/(3! x (7-3)!) x 4!/(3! x (4 - 3)!)

   = 35 x 4

   = 140 ways

Hope this helps!

:)

7

step-by-step explanation:

the answer would be 7