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

Computer Science

ScanSolve AI Answer

Answer

B

Step-by-step solution

3 steps

Here are the solutions to the problems:

Part 17· 1 step

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 nn distinct items is n!n!.
  • Here, n=8n=8.

  1. Calculate the factorial.

    8!=8×7×6×5×4×3×2×1=403208! = 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 40320\boxed{\text{40320}}.

Part 18· 2 steps

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)=103 \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.

  1. Use the combination formula (nk)=n!k!(n−k)!\binom{n}{k} = \frac{n!}{k!(n-k)!}.

    Here, n=10n=10 and k=4k=4.

    (104)=10!4!(10−4)!=10!4!6!\binom{10}{4} = \frac{10!}{4!(10-4)!} = \frac{10!}{4!6!}

  2. Calculate the value.

    (104)=10×9×8×74×3×2×1=10×3×7=210\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 210\boxed{\text{210}}.

Part 19

In how many ways can a teacher distribute 4 identical books to 4 students?

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