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!

:)

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step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

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i dont get the question

step-by-step explanation: