Question

On a banquet table, 11 different dishes of food will be placed in a row. There are 6 vegetarian dishes and 5 meat dishes. They will be placed alternating between the two types of dishes. A vegetarian dish will be first. How many ways are there to place the dishes on the table?

Answer 1

Okay, here we have this:

Considering the provided information, we are going to calculate the requested probability, so we obtain the following:

So to calculate the number of total possibilities, what we will do is multiply the number of possibilities of organizing the vegetarian ones by the number of possibilities of organizing the meat ones, then we have:

Number of ways to organize the dishes on the table =Number of ways to organize the meat * Number of ways to organize vegetarians

Number of ways to organize the dishes on the table =5! *6!

Number of ways to organize the dishes on the table =120 * 720

Number of ways to organize the dishes on the table =86400

Finally we get that there are 86400 ways to arrange the dishes on the table.