Please make sure that answers are right, very important!!! Discrete math!!!

. Question 1 > A standard deck of cards consists of four suits (clubs, diamonds, hearts, and spades), with each suit containing 13 cards (ace, two through ten, jack, queen, and king) for a total of 52 cards in all. (a) How many 9 card hands contain 5 hearts and 4 spades? (b) How many 9 card hands contain exactly 5 hearts? (c) How many 5 card hands contain 4 king(s) and 1 queen(s)? (d) How many 5 card hands contain exactly 4 king(s)?. Question 3 Consider a set of elements X1, ... X18. (a) How many 10-element subsets contain x? (b) How many 10-element subsets do not contain X9? (c) How many 10-element subsets contain x, and x, but do not contain X9?' Question I5 1* C ) A company received a shipment of 36 Laser printers, including it! that are defective. 8 of these printers are seLecteci to be used in the cop}...r room. {a} How many.r selections of B printers can be made? [b] How many seLections of B printers have no defective printers? . Question I" 1* A group of 8 students including Anna, Brett, Carlos, Deborah, and Edith will sit around a circular table. (a) How many different ways can the 8 students sit around the circular table? I.e. how many circular permutations are there of the 8 students? (b) How many ways can they do this if the triple (Anna, Brett, Carlos) must sit together (in any order) and the pair (Deborah, Edith) must sit together (in any order)? (c) How many ways can they do this if the triple (Anna, Brett, Carlos) must sit together (with Brett in the middle) and the pair (Deborah, Edith) must sit together (in any order)?. Question 10 1* A strictly monotonic lattice path with steps size 1 in two-space consists of a sequence of steps where each step increases either the -coordinate or the y-coordinate while leaving the other coordinate unchanged. (a) How many strictly monotonic lattice paths with step size 1 are there from (6, 2) to (16, 28)? (b) How many of these paths from (6, 2) to (16, 28) pass through the point (11, 11)? (c) How many of these paths from (6, 2) to (16, 28) avoid the point (11, 11)?. Question 14 A jewelry case contains 12 necklaces, 8 rings, and 5 bracelets all are distinguishable. A person selects 6 pieces of jewelry from the case. (a) How many different selections are possible with exactly 2 bracelets? (b) How many different selections are possible if at least 3 piece(s) of jewelry must be bracelets? (c) How many different selections are possible if at most 3 piece(s) of jewelry must be bracelets?. Question 1? 1* 1C > A strictly monotonic lattice path with steps size 1 in two-space consists of a sequence of steps where each step increases either the alt-coordinate or the y-coordinate while leaving the other coordinate unchanged. {a} How many.r strictlyr monotonic lattice paths with step size 1 are there from [1&3] to [23, 27]? [b] How many of these paths from [1i], 3:] to {23, 27} pass through the point {15, 15]? [c]: HOW many.r of these paths from [1&3] to [23, 2?] avoid the point (15,15)