Suppose we want to form shopping lists out of the following three sets of items,
ID: 3302139 • Letter: S
Question
Suppose we want to form shopping lists out of the following three sets of items, so that each list contains precisely one item from each set A_1, A_2, A_3. A_1 = {'water', 'beer', 'wine'}. A_2 = {'chocolate', 'ice cream'}, A_3 = {'apple', 'pear', peach', banana"} a) What are the distinct numbers of possible shopping lists we can obtain in this way, assuming that the way we order the items does not matter? b) How does the number of possible shopping lists change if the order the items are written down on the list does matter?Explanation / Answer
a) Total number of ways that we can make the shopping list ( Note that here we have to take exactly 1 element from each of the 3 sets )
= ( Total number of elements in A1)*(Total number of elements in A2)*(Total number of elements in A3)
= 3*2*4
= 24
Therefore there are 24 ways in which the shopping list could be made.
b) Now in case the order also matters, the total permutations of 3 items is computed to be 3! = 6 for example for 3 items XYZ the possible permutations could be : XYZ, XZY, YZX, YXZ, ZXY, and ZYX therefore there are 6 permutations for each selection. Therefore the total number of possible shopping lists here would be computed as: = 24*6 = 144
Therefore there are 144 ways in which the shopping list could be made.