Aprize bag contains 1 hologram pencil, 7 blue-striped pencils, and 2 flowered pencils. if two pencils are randomly chosen from the prize bag, how many different color combinations are possible?

45 different color combinations are possible if two pencils are randomly chosen from the prize bag.

Step-by-step explanation:

The bag contains 1 hologram pencil + 7 blue-striped pencils + 2 flowered pencils.

So, the prize bag contains 10 pencils in total.

Combination formula C(n,r)= n!/r!(n-r)!

where n= 10 pencils, Out of these 10 pencils, only 2 pencils are randomly chosen. So, r= 2.

The 10 pencils can be arranged in 10! (10*9*8*7*6*5*4*3*2*1) ways.

C(10,2)= 10!/(2!)(10-2)!

            = 10!/(2!)(8!) = 10*9*8!/ 2!*8!

                                  = 10*9/ 2*1

                                  = (5*9)= 45 different combinations.

the correct answer is the second option