(a) there are $n$ chairs in a row. find the number of ways of choosing $k$ of these chairs, so that no two chosen chairs are adjacent. (b) there are 10 chairs in a circle, labelled from 1 to 10. find the number of ways of choosing 3 of these chairs, so that no two chosen chairs are adjacent. (c) there are $n$ chairs in a circle, labelled from 1 to $n.$ find the number of ways of choosing $k$ of these chairs, so that no two chosen chairs are adjacent.

Cadbury has a chocolate factory in dunedin, new zealand. for easter, it makes two kinds of “easter eggs”: milk chocolate and dark chocolate. it cycles between producing milk and dark chocolate eggs. the table below provides data on these two products. demand (lbs per hour) milk: 500 dark: 200 switchover time (minutes) milk: 60 dark: 30 production rate per hour milk: 800 dark: 800 for example, it takes 30 minutes to switch production from milk to dark chocolate. demand for milk chocolate is higher (500lbs per hour versus 200 lbs per hour), but the line produces them at the same rate (when operating): 800 lbs per hour. a : suppose cadbury produces 2,334lbs milk chocolate and 1,652 lbs of dark chocolate in each cycle. what would be the maximum inventory (lbs) of milk chocolate? b : how many lbs of milk and dark chocolate should be produced with each cycle so as to satisfy demand while minimizing inventory?