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}

  • View Answer
  • Comment on this question

• 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}

  • View Answer
  • Comment on this question

• 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}

  • View Answer
  • Comment on this question

• 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}

  • View Answer
  • Comment on this question

• 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}

  • View Answer
  • Comment on this question

• 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}

  • View Answer
  • Comment on this question

• 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}

  • View Answer
  • Comment on this question