This is a three part question Please answer each portion sho

This is a three part question. Please answer each portion, show all work and formulas to arrive at final answer. Thanks, will rate quickly.

Your tour group of 40 people stops at a local restaurant.

a.) The restaurant can only accept 16, the rest will have to cross the street to another place. How many ways can you select 16 people out of your 40?

b.) Once seated, you find that you may make a selection of one item each from three columns of offerings: 4 salads, 3 entrees and 4 desserts. How many different meals can you create?

c.) After the meal, you line up for the group photo, 8 at a time, in order from smallest to largest. How many ways could you take the first photo?

Solution

a)

There are

40C16 = 40!/(16!24!) = 62852101650 ways.

b)

As the choices are independent, you can create 4*3*4 = 48 meals.

c)

When you select 8 from your group of 16, there\'s only 1 way to reorder the 8 from smallest to biggest.

Thus, it\'s like order does not matter (as you count each combination just once).

Thus, there are 18C6 = 18!/(8!8!) = 12870 ways.