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1. let n be a natural number compute the number of permutations s:{1,...,3n}->{1,...,3n} on 3n terms that satisfies s(n)<s(2n)<s(3n).

2. compute the number of permutations s:{1,...,n}->{1,..,n} that satisfy: for every i,j in 1,..,n |s(k)-s(j)|<=|k-j|

for the first question i found that the answer is first we calculate the permutations where every member in the set gets permuted except for n,2n,3n which is (3n-3)! now for the other three we choose the biggest to be s(3n) and so on, so the answer is (3n-3)!/

now for second question, i got that in order to satsfy this condition the follow should be met:

either 1<=s(k)<=k and j<=s(j)<=n or k<=s(k)<=n and 1<=s(j)<=j

i think that this is correct but i dont know how to use it to calculate the number of permutations, any tips, hints?

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# Some permutations.

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