Final answer:
There are 252 sets of size 5 and 2002 multisets of size 5 that can be made using the 10 numeric digits 0 through 9.
Step-by-step explanation:
A set of size 5 can be made using the 10 numeric digits 0 through 9 by selecting 5 digits from the set without repetition. This can be done using the concept of combinations. The number of combinations of 10 objects taken 5 at a time is given by the formula:
C(10, 5) = 10! / (5! * (10-5)!) = 252
Therefore, there are 252 sets of size 5 that can be made using the 10 numeric digits 0 through 9.
A multiset of size 5 can be made using the 10 numeric digits 0 through 9 by selecting 5 digits from the set with repetition allowed. This can be done using the concept of combinations with repetition. The number of combinations with repetition of 10 objects taken 5 at a time is given by the formula:
C(10 + 5 - 1, 5) = C(14, 5) = 2002
Therefore, there are 2002 multisets of size 5 that can be made using the 10 numeric digits 0 through 9.
Complete question:
A multiset is a collection of objects, just like a set, but can contain an object more than once (the order of the elements still doesn’t matter). For example, {1,1,2,5,5,7} is a multiset of size 6.
1. How many sets of size 5 can be made using the 10 numeric digits 0 through 9?
2. How many multisets of size 5 can be made using the 10 numeric digits 0 through 9?