Permutation and Combination Questions Answers

• 1. Evaluate $$\begin{aligned} \frac{30!}{28!} \end{aligned}$$

  1. 970
  2. 870
  3. 770
  4. 670

  Answer And Explanation

  Answer: Option B

  Explanation:

  $$\begin{aligned} = \frac{30!}{28!} \\ = \frac{30 * 29 * 28!}{28!} \\ = 30 * 29 = 870 \end{aligned}$$

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• 2. Evaluate permutation equation
  $$\begin{aligned} ^{59}{P}_3 \end{aligned}$$

  1. 195052
  2. 195053
  3. 195054
  4. 185054

  Answer And Explanation

  Answer: Option C

  Explanation:

  $$\begin{aligned} ^n{P}_r = \frac{n!}{(n-r)!} \\ ^{59}{P}_3 = \frac{59!}{(56)!} \\ = \frac{59 * 58 * 57 * 56!}{(56)!} \\ = 195054 \end{aligned}$$

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• 3. Evaluate permutation
  $$\begin{aligned} ^5{P}_5 \end{aligned}$$

  1. 120
  2. 110
  3. 98
  4. 24

  Answer And Explanation

  Answer: Option A

  Explanation:

  $$\begin{aligned} ^n{P}_n = n! \\ ^5{P}_5 = 5*4*3*2*1 \\ = 120 \end{aligned}$$

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• 4. Evaluate permutation equation
  $$\begin{aligned} ^{75}{P}_2\end{aligned}$$

  1. 5200
  2. 5300
  3. 5450
  4. 5550

  Answer And Explanation

  Answer: Option D

  Explanation:

  $$\begin{aligned} ^n{P}_r = \frac{n!}{(n-r)!} \\ ^{75}{P}_2 = \frac{75!}{(75-2)!} \\ = \frac{75*74*73!}{(73)!} \\ = 5550 \end{aligned}$$

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• 5. Evaluate combination
  $$\begin{aligned} ^{100}{C}_{97} = \frac{100!}{(97)!(3)!} \\ \end{aligned}$$

  1. 161700
  2. 151700
  3. 141700
  4. 131700

  Answer And Explanation

  Answer: Option A

  Explanation:

  $$\begin{aligned} ^{n}{C}_r = \frac{n!}{(r)!(n-r)!} \\ ^{100}{C}_{97} = \frac{100!}{(97)!(3)!} \\ = \frac{100*99*98*97!}{(97)!(3)!} \\ = \frac{100*99*98}{3*2*1} \\ = \frac{100*99*98}{3*2*1} \\ = 161700 \end{aligned}$$

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• 6. Evaluate combination
  $$\begin{aligned} ^{100}{C}_{100} \end{aligned}$$

  1. 10000
  2. 1000
  3. 10
  4. 1

  Answer And Explanation

  Answer: Option D

  Explanation:

  $$\begin{aligned} ^{n}{C}_{n} = 1 \\ ^{100}{C}_{100} = 1 \end{aligned}$$

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• 7. How many words can be formed by using all letters of TIHAR

  1. 100
  2. 120
  3. 140
  4. 160

  Answer And Explanation

  Answer: Option B

  Explanation:

  First thing to understand in this question is that it is a permutation question.
  Total number of words = 5
  Required number =
  $$\begin{aligned} ^5{P}_5 = 5! \\ = 5*4*3*2*1 = 120 \end{aligned}$$

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