Final answer:
To find the 50th and 100th permutations of the numbers 1, 2, 3, 4, 5 in lexicographical and reverse lexicographical order, list all the permutations and find the ones that correspond to the desired positions.
Step-by-step explanation:
To find the 50th and 100th permutations of the numbers 1, 2, 3, 4, 5 in lexicographical order, we can list all the possible permutations and then find the ones that correspond to the desired positions. Let's go step by step:
- Arrange the numbers in ascending order: 1, 2, 3, 4, 5.
- List all the possible permutations: 12345, 12354, 12435, 12453, 12534, 12543, ..., 54321.
- The 50th permutation will be 41523.
- The 100th permutation will be 54321.
To find the 50th and 100th permutations in reverse lexicographical order, we can list all the possible permutations starting from the highest number and going in reverse order. The 50th permutation will be 21534 and the 100th permutation will be 12345.