Example 7: Use a tree diagram to find the possible three-digit numbers than can be written using only the digits 1, 2, and 3. Assume repeated digits are NOT allowed. [Note: This process will be referred to as "without replacement".] Part I: Part II: Part III: Select the first digit Select the second digit Select the third digit

The set, S consists of 900,000000 whole numbers, each being the same number of digits long. How many digits long is a number from S? (Hint: use the fact that a whole number cannot start with the digit 0.)

In Example 10, the team must consist of six boys and six girls. How many different 12-member teams are possible?

A product’s catalog number is made up of one letter from the English alphabet followed by a five-digit number. How many different catalog numbers are possible?

How many arrangements can be made from the letters of the word “mountains” if all the vowels must form a string?

How many ways can a committee of 3 freshmen and 4 juniors be formed from a group of 8 freshmen and 11 juniors?

How many subsets does the set 1,3,5,...,99 have?

How many distinct ways can the word EVANESCENCE be arranged if the anagram must end with the letter E?