Final answer:
To find the number of different requests possible if a customer can request up to 3 free samples out of 13 offers, use the formula for combinations without repetition: nCr = n! / (r!(n-r)!), where n is the total number of items and r is the number of items selected.
Step-by-step explanation:
To find the number of different requests possible if a customer can request up to 3 free samples out of 13 offers, we will use the concept of combinations. Since the order of the samples does not matter, we will use combinations without repetition.
The formula for combinations without repetition is nCr = n! / (r!(n-r)!), where n is the total number of items and r is the number of items selected. In this case, n = 13 (number of offers) and r can be 1, 2, or 3 (number of free samples requested).
Therefore, the number of different requests possible for 1 free sample is 13C1 = 13! / (1!(13-1)!). Similarly, the number of different requests possible for 2 free samples is 13C2 = 13! / (2!(13-2)!), and the number of different requests possible for 3 free samples is 13C3 = 13! / (3!(13-3)!).