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

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Advance Math

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

  1. The manager at Mike's Place needs to choose 5 Molson brands and5 Labatt brands to sell. How many options do they have?
  2. The 10 beers (5 Labatt, 5 Molson) selected in the previousquestion must be placed in a line on a display shelf so that no twoMolson products are adjacent and no two Labatt products areadjacent. How many ways are there to do this?
  3. 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?
  4. How many of the arrangements from the previous question havethe bottle of 50 and the bottle of Export among the first(leftmost) 5 bottles?

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