Permutation and Combination: Test 2

10 questions · 15 minutes · scoring and calculator rules shown before you begin

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Permutation and Combination Test 2: questions and answers

Take the test first if you want an honest score. The answers and solutions below are folded away until you open them.

  1. 1. In how many different ways can the letters of the word 'PLANET' be arranged?
    1. 120
    2. 360
    3. 720
    4. 36

    Reference: q-f9dbe27a-77 · Report this question

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    Answer: C. 720

    The word has 6 different letters, so the number of arrangements is 6! = 720.
  2. 2. In how many different ways can the letters of the word 'PEPPER' be arranged?
    1. 30
    2. 720
    3. 120
    4. 60

    Reference: q-6783d3a4-77 · Report this question

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    Answer: D. 60

    There are 6 letters with P repeated 3 times and E repeated 2 times. Arrangements = 6! / (3! × 2!) = 60.
  3. 3. In how many ways can a committee of 2 members be selected from 11 persons?
    1. 110
    2. 73
    3. 55
    4. 22

    Reference: q-6c76c9ec-75 · Report this question

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    Answer: C. 55

    Number of ways = 11C2 = 55.
  4. 4. In how many ways can a committee of 3 men and 2 women be formed from 5 men and 4 women?
    1. 126
    2. 78
    3. 60
    4. 16

    Reference: q-1384e7e1-88 · Report this question

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    Answer: C. 60

    Men can be chosen in 5C3 = 10 ways and women in 4C2 = 6 ways. Total = 10 × 6 = 60.
  5. 5. 18 people attend a meeting and each shakes hands with every other person exactly once. How many handshakes take place?
    1. 306
    2. 153
    3. 151
    4. 324

    Reference: q-9e3e84f5-119 · Report this question

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    Answer: B. 153

    Number of handshakes = 18C2 = 18 × 17 / 2 = 153.
  6. 6. In how many different ways can the letters of the word 'MANGO' be arranged?
    1. 120
    2. 25
    3. 60
    4. 24

    Reference: q-e0d38ed4-76 · Report this question

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    Answer: A. 120

    The word has 5 different letters, so the number of arrangements is 5! = 120.
  7. 7. In how many different ways can the letters of the word 'SUMMER' be arranged?
    1. 720
    2. 180
    3. 480
    4. 360

    Reference: q-3d7d0809-77 · Report this question

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    Answer: D. 360

    There are 6 letters with M repeated 2 times. Arrangements = 6! / (2!) = 360.
  8. 8. In how many ways can a committee of 3 members be selected from 8 persons?
    1. 336
    2. 24
    3. 44
    4. 56

    Reference: q-c10d65e3-74 · Report this question

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    Answer: D. 56

    Number of ways = 8C3 = 56.
  9. 9. In how many ways can a committee of 2 men and 1 woman be formed from 8 men and 5 women?
    1. 33
    2. 140
    3. 286
    4. 112

    Reference: q-8479d3c3-88 · Report this question

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    Answer: B. 140

    Men can be chosen in 8C2 = 28 ways and women in 5C1 = 5 ways. Total = 28 × 5 = 140.
  10. 10. In how many ways can 4 persons be seated around a round table?
    1. 24
    2. 12
    3. 7
    4. 6

    Reference: q-8cecfc4f-63 · Report this question

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    Answer: D. 6

    Arrangements around a circle = (n − 1)! = 3! = 6.

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