Molson currently sells 41 different brands of beer in Canada. Labatt currently sells 17 different brands....

Molson currently sells 41 different brands of beer in Canada. Labatt currently sells 17 different brands. The manager at Mike's Place 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 a display shelf so that no two Molson products are adjacent and no two Labatt products are adjacent. How many ways are there to do this? Continuing from the previous question, suppose two of the brands selected by the manager were (Labatt) 50 and (Molson) Export. The display shelf can not have a bottle of 50 adjacent to a bottle of Export. How many ways are there to do this while still avoiding two adjacent Molson products and two adjacent Labatt products? How many of the arrangements from the previous question have the bottle of 50 and the bottle of Export among the first (leftmost) 5 bottles?

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Colby Messinger answered 1 year ago

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