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!

:)

the answer would be d.

step-by-step explanation:

move all variables to the left side and all constants to the right side

(x−3)^2+(y−1)^2=16

this is the form of a circle. use this form to determine the center and radius of the circle.

( x − h ) 2 + ( y − k ) 2 = r 2

match the values in this circle to those of the standard form. the variable   r   represents the radius of the circle,   h   represents the x-offset from the origin, and   k   represents the y-offset from origin.

r = 4

h = 3

k = 1

the center of the circle is found at   ( h , k ) .

center:   ( 3 , 1 )

these values represent the important values for graphing and analyzing a circle.

center:   ( 3 , 1 ).

radius:   4