- If you choose one item from a group of M items, and one item from a group of N items, then you have a total of M*N possible combinations.
- I pick a book from a shelf containing 3 books (The Hobbit, War and Peace, Beowulf) and pick a drink from a list of two drinks (Coke, Tea). How many different combinations can I have.
+-------- Tea
+---The Hobbit-----|
| +-------- Coke
+
| +-------- Tea
--+---War and Peace--|
| +-------- Coke
+
| +-------- Tea
+---Beowulf -------|
+-------- Coke
There are 3x2 or 6 possibilities.
- Example: In an experiment, I flip a coin and toss a 6 sided dice. How many results can I have?
There are two ways to flip a coin (H, T)
There are six ways to roll a dice (1,2,3,4,5,6)
So there are 2x6 or 12 different results.
- Example: There are 25 women and 13 men in this class. How many ways can I form a committee of one man and one woman?
13 x 25 = 325
- This can be extended to multiple sets
- Example: When purchasing a pen, I have a choice of 4 colors (red, black, orange, green), two types of tips (fine, normal, bold), and two permanency varieties (erasable, permanent). How many different types of pens can I purchase?
|
+------------------+--------------------+
| |
E P
+----------+---------+ +----------+- -------+
f n b f n b
+-+-+-+-+ +-+-+-+-+ +-+-+-+-+ +-+-+-+-+ +-+-+-+-+ +-+-+-+-+
r b o g r b o g r b o g r b o g r b o g r b o g
2 x 3 x 4 = 24 choices.
- How many three letter passwords can I have? (Use only upper case letters)
There are 26 upper case letters, so I can have
26 choices for the first letter
26 choices for the second letter
26 choices for the third letter.
26 x 26 x 26 = 263 = 17,576 choices
- How about a 4 letter password, with upper case, lower case and numbers?
there are 26+26+10 = 62 different choices for each spot, and there are 4 spots.
624 = 14,776,336
- Repeat the above problem, but you can't start with a digit.
For the first space there are now only 52 choices.
For every other space there are still 62 choices
52 x 62 x 62 x 62 = 12,393,056 choices
- How many four letter radio stations call letters can be formed if the first letter must be W or K? (upper case only)
2 x 26 x 26 x 26 = 35,152 stations