Thus, there are $ \boxed{25} $ ways.
Related Articles
- Question: A renewable energy engineer designs a piezoelectric road with 5 identical sensors. How many ways can these sensors be partitioned into 3 non-empty, indistinct groups to optimize power distribution?
- Solution: This requires the Stirling numbers of the second kind $ S(5, 3) $, which count the ways to partition 5 distinguishable objects into 3 non-empty indistinct subsets. Using the recurrence relation:
- S(5, 3) = S(4, 2) + 3 \times S(4, 3) = 7 + 3 \times 6 = 25
- Question: A computational biologist studies a genome with 8 genes. How many ways can 3 genes be selected for further analysis if the order of selection does not matter?
- Solution: The number of ways to choose 3 genes from 8 is given by the combination formula:
- Thus, there are $ \boxed{56} $ possible selections.
