Final answer:
For part (i) where the cones are different flavors, there are 360 ways a customer can choose 4 ice-cream cones. For part (ii) where the cones are not necessarily of different flavors, there are 1296 ways a customer can choose 4 ice-cream cones.
Step-by-step explanation:
To find the number of ways a customer can choose 4 ice-cream cones, we can use the concept of combinations. For part (i), where the cones are all different flavors, we can use the formula for combinations: nCr = n! / (r!(n-r)!), where n is the number of flavors and r is the number of cones chosen. In this case, n = 6 and r = 4. So the number of ways is 6C4 = 6! / (4!(6-4)!) = 6! / (4!2!) = (6*5*4*3) / (4*3*2*1) = 360 ways.
For part (ii), where the cones are not necessarily of different flavors, we can still use combinations. In this case, each cone can be chosen from any of the 6 flavors, so there are 6 choices for each of the 4 cones. So the number of ways is 6^4 = 6 * 6 * 6 * 6 = 1296 ways.