A box contains 12 light bulbs. Find the number n of ordered samples of size 3: (a) with replacement; (b) without replacement/
(a) With replacement:
Each light bulb can be chosen 3 times (since we are sampling with replacement), so for each bulb, there are 12 possible choices. Thus, the total number of samples is:
n = 12 x 12 x 12 = 1,728
(b) Without replacement:
For the first bulb, we have 12 choices. For the second bulb, we have 11 remaining choices. Finally, for the third bulb, we have 10 remaining choices. Thus, the total number of samples is:
n = 12 x 11 x 10 = 1,320