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.
