Question 17: How many different ways can you arrange the letters of the word COMPUTER?

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 × 7 × 6 × 5 × 4 × 3 × 2 × 1 = 40320 The correct option is b). The final answer is 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 (red) + 7 (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 nk = (n!)/(k!(n-k)!). Here, n=10 and k=4. 104 = (10!)/(4!(10-4)!) = (10!)/(4!6!) Step 2: Calculate the value. 104 = (10 × 9 × 8 × 7)/(4 × 3 × 2 × 1) = 10 × 3 × 7 = 210 The correct option is b) or c). The final answer is 210. Question 19: In how many ways can a teacher distribute 4 identical books to 4 students?