Explain the correct answer

#1

I am not able to solve some questions. Can you please explain the correct answers of the following questions :

Question 4: From the set of numbers s={1, 2, 3, 4}, how many minimum numbers must be selected to guarantee that at least one pair of these numbers has a sum equal to 7?

Question 8: In how many ways 5 men and 3 women can sit together on a circle such that a particular men m1 and particular women w1 never sit adjacent to each other?

Question 10: Let x = a5 + b11 , where a>0 and b>0. What is the largest value of x that can not be made?

#2

@HemantKumar
Q4 : You need both 3 and 4 to be picked. If any is not picked you can’t make pair with 7. So you need to pick all numbers
Q8 : Based on cyclic permutation. Assume m1,w1 as one unit mw. Now total ways people can sit in circle is 6!. Since m1,w1 can be in 2 ways in mw so multiply 2. 2*6!. These are total ways in which m1,w1 sit together. Now total ways people could have been arranged is 7!. So total - not possible is possible. So ans is 7! - 2*6! = 5*6!
Q10 : Simply check for all 4 values if there is a combination to make that sum using 5 and 11