How do you do this? Math question

Question

A restaurant offers a choice of 5 salads, 8 main courses, and 4 deserts. How many possible 3-course meals are there?

Answer 1

If any three-course meal consists of one salad, one main dish and one dessert and there are no other restrictions regarding what can be combined, the answer is 160. Here's why.

 

There are five options for salads each of which can be combined with any of eight main courses. That means there are forty combinations of salad and main course (5 x 8 = 40). Each of these forty combinations may be combined with any of four desserts. Forty times four equals 160. All you really do to arrive at the answer is to multiply the three numbers of options (5 x 8 x 4 = 160).

Answer 2

First, remember that the decimal number system is a positional number system, so that there are, for example, ones place and tens place and hundreds place for the values 000-999 (that is, 10*10*10=1000) possible 3-digit numbers.  So, think of the possible numbers a counter could show when it displays exactly one of the numbers in each column:

0 0 0

1 1 1

2 2 2

3 3 3

4 4 4

5 5 5

6 6 6

7 7 7

8 8 8

9 9 9

If you want to drive someday, you may see such counters on a gas pump or an odometer.

 

This problem has a special counter with restricted values of digits, but you still have to pick one each from the three columns:

0 0 0

1 1 1

2 2 2

3 3 3

4 4

   5

   6

   7

 

There are 5*8*4=160 possible combinations  [note that the 5 digits used are 0-4, etc.]