Collective Arts Brewing currently makes 30 types of IPA and 6 types of Lager. The manager...

Collective Arts Brewing currently makes 30 types of IPA and 6 types of Lager.

The manager at Mike's Place needs to choose 4 types of IPA and 4 types of Lager. How many options does the manager have?
The 8 beers (4 IPA and 4 Lager) selected in the previous question must be placed in a line on a display shelf so that no two IPA are adjacent and no two Lager are adjacent. How many ways are there to do this?
Continuing from the previous question, suppose that two of the beers selected were All Together Now (an IPA) and Hot Pink (a Lager). Since both cans are pink, the manager doesn't want to place them adjacent to each other. How many ways are there to do this (while still alternating between IPA and Lager)?
How many of the arrangements from the previous question have the All Together Now among from the 4 leftmost bottles and the bottle of Hot Pink among the 4 rightmost bottles?

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Expert Solution

orchestra answered 1 year ago

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