Question

The general manager of a fast food restaurant chain must select 6 restaurants from 11 for a promotional program. How many different possible ways can this selection be done?

Answer 1

462

Explanation:

There 6 slots available to fill in the restaurants options

- For the 1st slot, there are 11 ways to choose

- For the 2nd slot, there are 10 ways to choose

- For the 3rd slot, there are 9

- For the 4th slot, there are 8

- For the 5th slot, there are 7

- For the last 6th, there are 6 ways

So in total there would be 11*10*9*8*7*6 = 332640 ways to choose. But since the order of these 6 slots don't matter, there are actually 6! = 720 ways to order these 6 slots. So the actual number of possible ways is

332640 / 720 = 462

Answer 2

Explanation:

This question will be solved using the combination formula which is nCr because the order is unimportant and we need the selection.

11C6

11!/(11-6)!*6!

= 462

Therefore the manager can select the restaurant in 462 ways.