Ask Question
21 October, 05:58

How many 4-permutations of [10] have maximum element equal to 6? How many have maximum element at most 6?

+2
Answers (1)
  1. 21 October, 09:10
    0
    I'm guessing that [10] refers to the set of the first 10 positive integers.

    If the largest element of a given 4-permutation is 6, then the other three elements are pulled from the set {1, 2, 3, 4, 5}. This can be done in 5! / (5 - 3) ! = 60 ways. Then there are four possible positions to place the 6, giving a total of 4 * 60 = 240 permutations.

    If the largest element of a permutation is * at most * 6, then the maximal element is 4, 5, or 6.

    If it's 4, then there are three other elements available; this can be done in 3! / (3 - 3) ! = 6 ways; multiply by 4 to get a total of 24; If it's 5, then there are four other elements available, hence 4! / (4 - 3) ! = 24 ways; multiply by 4 to get a total of 96; If it's 6, then the total is 240.

    Putting everything together, the total number of permutations in which the maximal element is at most 6 is 24 + 96 + 240 = 360.
Know the Answer?
Not Sure About the Answer?
Find an answer to your question ✅ “How many 4-permutations of [10] have maximum element equal to 6? How many have maximum element at most 6? ...” in 📘 Mathematics if you're in doubt about the correctness of the answers or there's no answer, then try to use the smart search and find answers to the similar questions.
Search for Other Answers