The Brass Tap stocks 12 different beers, which it rotates randomly among its 8 taps. They will have one beer for each tap, and no two taps will have the same beer on any given evening. How many different beer menus do they need to stock.
12!/8!4!
bobpursley Thank you! I get easily miss lead by wording between combination and permutations problems
To determine the number of different beer menus the Brass Tap needs to stock, we can use the concept of permutations.
Since there are 12 different beers in total and 8 taps, the first tap can be filled with any of the 12 beers. Once the first tap is chosen, there are 11 beers remaining for the second tap, 10 beers for the third tap, and so on.
To calculate the total number of different beer menus, we need to multiply the number of choices for each tap together. This is done by finding the product of all the numbers from 12 down to 5, since we have 8 taps.
Therefore, the number of different beer menus is:
12 * 11 * 10 * 9 * 8 * 7 * 6 * 5
Calculating this expression gives us:
95,040 different beer menus.
So the Brass Tap needs to stock at least 95,040 different beer menus.