Molson currently sells 41 different brands of beer in Canada.Labatt currently sells 17 different brands. The manager at Mike'sPlace needs to choose 5 Molson brands and 5 Labatt brands to sell.How many options do they have? The 10 beers (5 Labatt, 5 Molson)selected in the previous question must be placed in a line on adisplay shelf so that no two Molson products are adjacent and notwo Labatt products are adjacent. How many ways are there to dothis? Continuing from the previous question, suppose two of thebrands selected by the manager were (Labatt) 50 and (Molson)Export. The display shelf can not have a bottle of 50 adjacent to abottle of Export. How many ways are there to do this while stillavoiding two adjacent Molson products and two adjacent Labattproducts? How many of the arrangements from the previous questionhave the bottle of 50 and the bottle of Export among the first(leftmost) 5 bottles?
