Answer:
(a) 479,001,600 combinations (b) 95,040 combinations (c) 3,326,400 combinations
Step-by-step explanation:
(a) In the case we have 12 different elements to stack, the possible combinations can be calculated as a premutation of 12 elements:
P = 12! = 479,001,600 combinations
(b) If seven components are identical, we have a permutation with repetition.
We have 7!=5040 combinations that are the same, so there is only one unique out of 5040 combinations. We have to divide the total possible combinations by 5040.
P = 12! / 7! = 479,001,600 / 5,040 = 95,040 combinations
(c) In the same way, if we have 3 components of Type 1 and 4 components of Type 2 (and the others all different), we have 3!*4! = 144 combinations that are the same.
P = 12!/(3!*4!) = 479,001,600 / 144 = 3,326,400 combinations
