How many 4-permutations of the positive integers not exeeding 100 contain three consecutive integers k, , in the correct order
a) where these consecutive integers can perhaps be separated by other integers in the permutation?
b) where they are in consecutive positions in the permutation?
We know that the number of permutations with repetition for a is since for every 98 possible choices of k we have 97*4 possible 4-permutations, (arrangements) of k, and another number different from those 3.
But how can I compute the repreated permutations?
For instance, consider . Then some of the possible permutations are "1,2,3,4","4,1,2,3","1,4,2,3" which are also permutations for . I think that given a number k I should find the 4-permutations of k that are repeated in other permutations. Then i will need to multiply this value for 98, the number of total possible Ks and subtract this from the first result. But I do not know how can I compute them.
Sorry if the question has already been made, but my point of interest regards how to find the repetitions I am interested in.