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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}

  • 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}

  • 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}

  • 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}

  • 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}

  • 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}

  • 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}