We want to select different sets of 5 pencils from a box of 12 distinct pencils. In this case, there is no order of arrangement. Combinations are used when there is no order or sequence of arrangement. We can pick 5 pencils without specifying if a particular color comes first. Thus, we would use combination. The combination formula for selecting r objects from n objects is expressed as
nCr = n!/r!(n - r)!
From the information given,
n = 12
r = 5
By substituting the values into the formula, we have
12C5 = 12!/5!(12 - 5)! = 12!/5!7!
12C5 = 792
Option D is correct