***DISCRETE MATH, PLEASE ONLY ANSWER IF YOU CAN ANSWER EVERY SINGLE QUESTION 1)F

Question

***DISCRETE MATH, PLEASE ONLY ANSWER IF YOU CAN ANSWER EVERY SINGLE QUESTION

1)For each permutation of {1, 2, 3, 4, 5, 6}, give the next largest permutation or indicate that the permutation is the last one in lexicographic order.

(a) (2,3,6,5,4,1)

(b) (2,3,6,1,4,5)

(c) (1,2,3,4,5,6)

(d) (6,5,4,3,2,1)

(e) (3,6,5,4,2,1)

2)For each 6-subset of 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, give the next largest 6-subset or indicate that the 6-subset is the last one in lexicographic order.

(a) {1,2,3,4,5,6}

(b) {1,4,6,10,11,12}

(c) {8,9,10,11,12,13}

(d) {1,4,6,11,12,13}

(e) {1,4,6,10,11,13}

Explanation / Answer

(1) Next permutation in Lexicographic order is

a) (2,3,6,5,4,1) => (2,4,1,3,5,6)

b) (2,3,6,1,4,5) => (2,3,6,1,5,4)

c) (1,2,3,4,5,6) => (1,2,3,4,6,5)

d) (6,5,4,3,2,1) => Last one in Lexicographic Order

e) (3,6,5,4,2,1) => (4,1,2,3,5,6)

(2) Next Largest 6-Subset of {1,2,3,4,5,6,7,8,9,10,11,12,13} in Lexicographic order for

a) {1,2,3,4,5,6} => {1,2,3,4,5,7}

b) {1,4,6,10,11,12} => {1,4,6,10,11,13}

c) {8,9,10,11,12,13} => Last one in Lexicographic Order

d) {1,4,6,11,12,13} => {1,4,7,11,12,13}

e) {1,4,6,10,11,13} =>{1,4,6,10,12,13}

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