Please help me to understand those two problems. Show all steps

.E M5 11]. In he'll.r man},r ways can 3 people be seated in a rotar if {a} there are no restrictions on the seating arrangement? {I1} persons A and 3 must sit next to each other? [1:] there are 4 men and 4 women and no 2 men or 2 women can sit next to each other? {11} there are 5 men and they.r must sit next to each other? {2} there are 4 married couples and each couple must sit together? For a combinatorial proof of the preceding. consider a set of n people and argue that both sides of the identity represent the number of different selections of a committee, its chair- person, and its secretary (possibly the same as the chairperson). Hint: (i) How many different selections result in the committee containing exactly & peo- ple? (ii) How many different selections are there in which the chairperson and the secre- tary are the same? (ANSWER: 12"-1.) (iii) How many different selections result in the chairperson and the secretary being different? (c) Now argue that E( R) 13 = 20-3n- (1 + 3 ) 13. Show that, for n > 0,Give a combinatorial argument (no computations are needed] to establish this identity. Him: Consider the set of numbers 1 through :1. Honr man},r subsets of size it have i as their highest- numbered member?r 12. Consider the following combinatorial identity: Eliza) =n . 2"-1 (a) Present a combinatorial argument for this identityr by considering a set of :1! people and determining? in two ways? the number of pos- sible selections of a committee of any size and a chairperson for the committee. Hint: {i} How man},r possible selections are there of a committee of size it and its chairper- son? {ii} How man},r possible selections are there of a chairperson and the other commit tee members? (h) Verify the following identity for n = 1+2? 3,4, 5: I! Z(:)kl =2"'2r:{r: +1]I k=l