Question

What is the rank,in lex order, of the permutation 6, 1, 2, 3, 4, 5?
क्रमचय 6, 1,2,3, 4, 5 के लेक्स ऑर्डर में रैंक​

Answer 1

Answer:

Accending number 1,2,3,4,5,6,

Answer 2

The permutation 6, 1, 2, 3, 4, 5 has a rank of 154 in the lexicographic order.

To Find:

the rank in lex order

Given:

permutation 6, 1, 2, 3, 4, 5

Solution:

We must count the number of permutations in lexicographic order that occur before a given permutation in order to determine its rank.

There are 5 leftover digits starting with the first one, 6, and since each of these numbers can appear in the initial place of a permutation, there are 5! = 120 permutations that begin with 6.

We then examine the second digit, which is 1. Due to the fact that we are only thinking about permutations that begin with 6, we may disregard the initial digit. There are 4 leftover digits, and since each of them can appear in the second place of a permutation, there are 4! = 24 permutations that begin with 61.

Keeping going in this manner, we arrive at the following permutation counts for each digit:

6: 5! = 120

1: 4! = 24

2: 3! = 6

3: 2! = 2

4: 1! = 1

5: 0! = 1 (there is only one permutation with one element)

We sum together these numbers to determine the overall number of permutations prior to 6, 1, 2, 3, and 4, in lexicographic order:

120 + 24 + 6 + 2 + 1 + 1 = 154

As a result, the permutation 6, 1, 2, 3, 4, 5 has a rank of 154 in the lexicographic order.

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