Application

4. If repetition is allowed, how many three-digit numbers can be formed using the digits 0, 1, 2, 3, 4, and 5? Explain your solution.

5. Find the number of ways of arranging the letters in the word DOMINATE if

a) there are no restrictions.

b) the first letter must be a vowel.

c) the last two letters must be T and E.

6. In how many ways could a group of 10 people form a committee with at least 8 people on it?