Please explain and show solving steps

Question 4 [30 marks] (a) Seiko, Seita and Saori visited Meshiya five day consecutively, and each day each of them ordered two different items on the menu. (i) Find the number ways could they make their order for these five days. [3 marks] (ii) Find the number ways could they make their order for these five days if if each of them didn't order the same item for two consecutive days. [3 marks] (iii) On one particular day when they visited Meshiya, seven other people also visited the eatery. If the eatery had exactly 10 seats in a row and all of them were randomly seated, find the probability that (A) three of them (Seiko, Seita and Saori) would sit next to each other. [4 marks] (B) exactly two of them would sit next to each other. [5 marks] (b) Yukiko can travel to Tokyo by either blue or green buses. The waiting times for these buses are both exponential, with means 10 minutes and 15 minutes respectively. The arrivals of these buses are independent of each other. (i) Find the probability that Yukiko will have to wait less than 10 minutes for a bus. [5 marks] (ii) Michiru brings Yukiko to her house. At her place they play a game where Yukiko has to randomly draw a card from a deck of 52 cards, then the draw cardis put back in the deck and throughly shuffled. They continue this procedure each time a card is drawn. (A) Find the probability that Yukiko draws exactly 3 diamonds in 5 attempts, given that she draws a diamond in the second attempt. [4 marks] (B) Find the expected number of attempts that needed to draw all the four different kings. [6 marks]Midnight Diner A small eatery called Meshiya, also referred to as the Midnight Diner, resides in the back alley of a bustling district. Despite the eatery's unusual hours, 12 am. to 7 am, a menagerie of customers ock to the establishment each night for a bite to eat and to Visit with the proprietor, known as the Master. While there is a menu, with only 4 items on its menu. Nevertheless, the Master makes whatever his customers request. As long as he has the ingredients for it. As patrons bond with the Master, they nd nourishment for their bellies and their souls. Below is the brief description of some of the characters in the story. Owner and chef of Meishiya. A literary editor who always wears mourning attire. Owner of a soba noodle restaurant whose son is in love with someone 15 ears his senior. Saori The lover of Seita Yukiko An old lady with dementia, loses two million yen after getting tricked by swindlers. Michiru The erson that takes Yukiko under her win