ReasoningAges 16-18

Ordered permutations P(n, 2)

Calculate ordered two-element permutations P(n, 2) = n(n − 1) from a set of distinct candidates. Review suitability for your learners before teaching.

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Worksheet StudioPractice pack · Ages 16-18

Ordered permutations P(n, 2)

Take your time. Show your thinking.

1. From 28 candidates, in how many ordered ways can a president and a vice-president be chosen?
28 · Ordered permutations P(n, 2)
2. From 17 candidates, in how many ordered ways can a president and a vice-president be chosen?
17 · Ordered permutations P(n, 2)
3. From 15 candidates, in how many ordered ways can a president and a vice-president be chosen?
15 · Ordered permutations P(n, 2)
4. From 6 candidates, in how many ordered ways can a president and a vice-president be chosen?
6 · Ordered permutations P(n, 2)
5. From 5 candidates, in how many ordered ways can a president and a vice-president be chosen?
5 · Ordered permutations P(n, 2)
6. From 8 candidates, in how many ordered ways can a president and a vice-president be chosen?
8 · Ordered permutations P(n, 2)
7. From 27 candidates, in how many ordered ways can a president and a vice-president be chosen?
27 · Ordered permutations P(n, 2)
8. From 22 candidates, in how many ordered ways can a president and a vice-president be chosen?
22 · Ordered permutations P(n, 2)
9. From 23 candidates, in how many ordered ways can a president and a vice-president be chosen?
23 · Ordered permutations P(n, 2)
10. From 26 candidates, in how many ordered ways can a president and a vice-president be chosen?
26 · Ordered permutations P(n, 2)
11. From 10 candidates, in how many ordered ways can a president and a vice-president be chosen?
10 · Ordered permutations P(n, 2)
12. From 25 candidates, in how many ordered ways can a president and a vice-president be chosen?
25 · Ordered permutations P(n, 2)

12 questions · Seed 104740 · Age guidance, not curriculum certification

View the answer key

Worksheet StudioAnswer key · Ages 16-18

Ordered permutations P(n, 2)

Answers and reasoning. Review before teaching.

1. From 28 candidates, in how many ordered ways can a president and a vice-president be chosen?
756
There are 28 choices for president and 27 remaining choices for vice-president: 28 × 27 = 756 ordered ways.
2. From 17 candidates, in how many ordered ways can a president and a vice-president be chosen?
272
There are 17 choices for president and 16 remaining choices for vice-president: 17 × 16 = 272 ordered ways.
3. From 15 candidates, in how many ordered ways can a president and a vice-president be chosen?
210
There are 15 choices for president and 14 remaining choices for vice-president: 15 × 14 = 210 ordered ways.
4. From 6 candidates, in how many ordered ways can a president and a vice-president be chosen?
30
There are 6 choices for president and 5 remaining choices for vice-president: 6 × 5 = 30 ordered ways.
5. From 5 candidates, in how many ordered ways can a president and a vice-president be chosen?
20
There are 5 choices for president and 4 remaining choices for vice-president: 5 × 4 = 20 ordered ways.
6. From 8 candidates, in how many ordered ways can a president and a vice-president be chosen?
56
There are 8 choices for president and 7 remaining choices for vice-president: 8 × 7 = 56 ordered ways.
7. From 27 candidates, in how many ordered ways can a president and a vice-president be chosen?
702
There are 27 choices for president and 26 remaining choices for vice-president: 27 × 26 = 702 ordered ways.
8. From 22 candidates, in how many ordered ways can a president and a vice-president be chosen?
462
There are 22 choices for president and 21 remaining choices for vice-president: 22 × 21 = 462 ordered ways.
9. From 23 candidates, in how many ordered ways can a president and a vice-president be chosen?
506
There are 23 choices for president and 22 remaining choices for vice-president: 23 × 22 = 506 ordered ways.
10. From 26 candidates, in how many ordered ways can a president and a vice-president be chosen?
650
There are 26 choices for president and 25 remaining choices for vice-president: 26 × 25 = 650 ordered ways.
11. From 10 candidates, in how many ordered ways can a president and a vice-president be chosen?
90
There are 10 choices for president and 9 remaining choices for vice-president: 10 × 9 = 90 ordered ways.
12. From 25 candidates, in how many ordered ways can a president and a vice-president be chosen?
600
There are 25 choices for president and 24 remaining choices for vice-president: 25 × 24 = 600 ordered ways.

12 questions · Seed 104740 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 16-18

Ordered permutations P(n, 2)

Take your time. Show your thinking.

1. From 28 candidates, in how many ordered ways can a president and a vice-president be chosen?
28 · Ordered permutations P(n, 2)
2. From 17 candidates, in how many ordered ways can a president and a vice-president be chosen?
17 · Ordered permutations P(n, 2)
3. From 15 candidates, in how many ordered ways can a president and a vice-president be chosen?
15 · Ordered permutations P(n, 2)
4. From 6 candidates, in how many ordered ways can a president and a vice-president be chosen?
6 · Ordered permutations P(n, 2)
5. From 5 candidates, in how many ordered ways can a president and a vice-president be chosen?
5 · Ordered permutations P(n, 2)
6. From 8 candidates, in how many ordered ways can a president and a vice-president be chosen?
8 · Ordered permutations P(n, 2)
7. From 27 candidates, in how many ordered ways can a president and a vice-president be chosen?
27 · Ordered permutations P(n, 2)
8. From 22 candidates, in how many ordered ways can a president and a vice-president be chosen?
22 · Ordered permutations P(n, 2)
9. From 23 candidates, in how many ordered ways can a president and a vice-president be chosen?
23 · Ordered permutations P(n, 2)
10. From 26 candidates, in how many ordered ways can a president and a vice-president be chosen?
26 · Ordered permutations P(n, 2)
11. From 10 candidates, in how many ordered ways can a president and a vice-president be chosen?
10 · Ordered permutations P(n, 2)
12. From 25 candidates, in how many ordered ways can a president and a vice-president be chosen?
25 · Ordered permutations P(n, 2)

12 questions · Seed 104740 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 16-18

Ordered permutations P(n, 2)

Answers and reasoning. Review before teaching.

1. From 28 candidates, in how many ordered ways can a president and a vice-president be chosen?
756
There are 28 choices for president and 27 remaining choices for vice-president: 28 × 27 = 756 ordered ways.
2. From 17 candidates, in how many ordered ways can a president and a vice-president be chosen?
272
There are 17 choices for president and 16 remaining choices for vice-president: 17 × 16 = 272 ordered ways.
3. From 15 candidates, in how many ordered ways can a president and a vice-president be chosen?
210
There are 15 choices for president and 14 remaining choices for vice-president: 15 × 14 = 210 ordered ways.
4. From 6 candidates, in how many ordered ways can a president and a vice-president be chosen?
30
There are 6 choices for president and 5 remaining choices for vice-president: 6 × 5 = 30 ordered ways.
5. From 5 candidates, in how many ordered ways can a president and a vice-president be chosen?
20
There are 5 choices for president and 4 remaining choices for vice-president: 5 × 4 = 20 ordered ways.
6. From 8 candidates, in how many ordered ways can a president and a vice-president be chosen?
56
There are 8 choices for president and 7 remaining choices for vice-president: 8 × 7 = 56 ordered ways.
7. From 27 candidates, in how many ordered ways can a president and a vice-president be chosen?
702
There are 27 choices for president and 26 remaining choices for vice-president: 27 × 26 = 702 ordered ways.
8. From 22 candidates, in how many ordered ways can a president and a vice-president be chosen?
462
There are 22 choices for president and 21 remaining choices for vice-president: 22 × 21 = 462 ordered ways.
9. From 23 candidates, in how many ordered ways can a president and a vice-president be chosen?
506
There are 23 choices for president and 22 remaining choices for vice-president: 23 × 22 = 506 ordered ways.
10. From 26 candidates, in how many ordered ways can a president and a vice-president be chosen?
650
There are 26 choices for president and 25 remaining choices for vice-president: 26 × 25 = 650 ordered ways.
11. From 10 candidates, in how many ordered ways can a president and a vice-president be chosen?
90
There are 10 choices for president and 9 remaining choices for vice-president: 10 × 9 = 90 ordered ways.
12. From 25 candidates, in how many ordered ways can a president and a vice-president be chosen?
600
There are 25 choices for president and 24 remaining choices for vice-president: 25 × 24 = 600 ordered ways.

12 questions · Seed 104740 · Age guidance, not curriculum certification