A local government is managing ads aimed at improving public health awareness. The government pays a social networking app to show its ads in users' news feeds. The social networking app has a variety of adds to show. If the government pays a fee, the app will guarantee that the ad will be shown, but that the add will be randomly mixed with other ads. The government believes they will improve health outcomes if users see two consecutive ads with health initiatives. The app will show a user precisely one ad each minute. The app's algorithm also states that if an ad has been shown then it will not be shown to the user again. The social media site shows all ads that it has been contracted to display. The app is currently contracted to display 5 health-related ads and 11 ads that are not health initiatives. Every ad is considered 'unique', i.e. there are no repetitions. i. How many ways can the app arrange these ads? ii. How many ways can the app arrange these ads, where there are at least two health ads in a row? iii. How many ads should the government have in their portfolio if they wish to ensure there is a probability of at least 0.5 of a user seeing at least two of their ads in a row? [1 mark for notation, definitions, rules, and working; 1 mark each for i, ii, iii] use Combinatorics