9. Given the word HEARINGS, in how many ways can 4 letters be arranged if (a) there are no restrictions; (b) there must be at least one vowel. 10. Using all the digits 0, 2, 2, 2, 3, 5, 5, how many even numbers can be formed? 1st reminder: A 0 is not allowed at the beginning. 2nd reminder: Consider the case of 0 at the end and the case of 2 at the end. 11. In how many ways can 7 students be arranged in a row if Anna, Bill and Carla must never sit beside each other? Hint: Position the 3 students as shown Then determine in how many A B C ways they can move around and still be separated from each other.12. A student saw this question on a test: How many 3-digit odd numbers can be formed from the digits 0, 1, 2, 3, 4, 5? The student said, "It's easy. The answer is _5_x_4_x_3_=60." S The last position can be a 1, 3, or 5. After filling the last position, there are 5 digits left for the Ist position. What mistake is the student making? Explain in a written sentence. What should the student have written instead