Here are the solutions to the problems: Question 17: How many different ways can you arrange the letters of the word COMPUTER? The word COMPUTER has 8 distinct letters. The number of ways to arrange $n$ distinct items is $n!$. Here, $n=8$. Step 1: Calculate the factorial. $$8! = 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 40320$$ The correct option is b). The final answer is $\boxed{\text{40320}}$. Question 18: If there are 3 red balls and 7 blue balls, how many ways can 4 balls be drawn without replacement? Total number of balls = $3 \text{ (red)} + 7 \text{ (blue)} = 10$ balls. We need to choose 4 balls from these 10. Since the order of drawing does not matter, this is a combination problem. Step 1: Use the combination formula $\binom{n}{k} = \frac{n!}{k!(n-k)!}$. Here, $n=10$ and $k=4$. $$\binom{10}{4} = \frac{10!}{4!(10-4)!} = \frac{10!}{4!6!}$$ Step 2: Calculate the value. $$\binom{10}{4} = \frac{10 \times 9 \times 8 \times 7}{4 \times 3 \times 2 \times 1} = 10 \times 3 \times 7 = 210$$ The correct option is b) or c). The final answer is $\boxed{\text{210}}$. Question 19: In how many ways can a teacher distribute 4 identical books to 4 students?