Suppose we want to find number of permutations x1, x2, ... x10 of numbers 1, 2,...

 

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Suppose we want to find number of permutations x1, x2, ... x10 of numbers 1, 2, ..., 10. But there is a restriction for some of the numbers to be placed in some of the positions as follows: xii 3 for all i = 1, 2, ... , 10 For example, permutation 10, 9, 1, 2, 5, 3, 6, 4, 7,8 is not acceptable since x8 greater than equal 5 (x8 8 - 3 = 5). How many of such permutations do exist? Justify your answer. = 4 but it must be Suppose we want to find number of permutations x1, x2, ... x10 of numbers 1, 2, ..., 10. But there is a restriction for some of the numbers to be placed in some of the positions as follows: xii 3 for all i = 1, 2, ... , 10 For example, permutation 10, 9, 1, 2, 5, 3, 6, 4, 7,8 is not acceptable since x8 greater than equal 5 (x8 8 - 3 = 5). How many of such permutations do exist? Justify your answer. = 4 but it must be