mba.com question on combinations

[shantascherla]

The lunch menu at a restaurant consists of 4 different entrees and 5 different side dishes

If a meal consists of 1 main course and 2 different side dishes how many combinations can be chosen

10
20
40
80
100

Answer 40

I approached this question in the prep using the slot machine approach

So for the maincourse he has 4 options and for the first side dish 5 and the second dish 4

So it came to 80

I then tried the combn approach for the side dishes C5/2 and reached to a 40 answer which matches the solution

My question is why the slot approach didnt work here ?

[sfbay]

you can watch "study hall with Ron" December 3, 2009 for a refresher on combinatorics.

http://www.manhattangmat.com/thursdays-with-ron.cfm



slot method - you need to divide the side dishes by 2! to eliminate double counting of 'peas and carrots' or 'carrots and peas'

[shantascherla]

Thanks got it

[jnelson0612]

Thanks munny.