Amath teacher assigns 3 projects. she gives the students 5 project options to choose frorm how many different groups of projects can the students choose from?

10

Step-by-step explanation:

This is a combination problem since the order does not matter.

nCr = n! / r! * (n - r)!  

where n is the number of things  (5 projects)

and r is the number of things chosen

! means factorial which is multiply that number and all the numbers below it

5C3 = 5!                     5!            5*4*3*2*1

                 =   =  

          3! ((5-3)!         3!  2!         3*2*1 (2*1)

Canceling like terms leaves

5C3 = 5*4/2 = 20/2 = 10

b. an equilateral triangle inscribed in a circle

step-by-step explanation:

we are given the figure of two circles having a triangle inside.

now, we know that,

"when a figure is lying inside an another figure, then the outside figure is known as circumscribed figure and the figure lying inside is referred to as the inscribed figure".

as we see that, the circles are containing the triangle completely.

thus, the circles are the circumscribed figures and the triangle is the inscribed figure.

hence, we get, 'an equilateral triangle is inscribed in a circle'.