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 20 candidates, in how many ordered ways can a president and a vice-president be chosen?
20 · Ordered permutations P(n, 2)
2. From 4 candidates, in how many ordered ways can a president and a vice-president be chosen?
4 · Ordered permutations P(n, 2)
3. From 28 candidates, in how many ordered ways can a president and a vice-president be chosen?
28 · Ordered permutations P(n, 2)
4. From 14 candidates, in how many ordered ways can a president and a vice-president be chosen?
14 · Ordered permutations P(n, 2)
5. From 8 candidates, in how many ordered ways can a president and a vice-president be chosen?
8 · Ordered permutations P(n, 2)
6. From 10 candidates, in how many ordered ways can a president and a vice-president be chosen?
10 · Ordered permutations P(n, 2)
7. From 15 candidates, in how many ordered ways can a president and a vice-president be chosen?
15 · Ordered permutations P(n, 2)
8. From 5 candidates, in how many ordered ways can a president and a vice-president be chosen?
5 · Ordered permutations P(n, 2)
9. From 18 candidates, in how many ordered ways can a president and a vice-president be chosen?
18 · Ordered permutations P(n, 2)
10. From 30 candidates, in how many ordered ways can a president and a vice-president be chosen?
30 · Ordered permutations P(n, 2)
11. From 26 candidates, in how many ordered ways can a president and a vice-president be chosen?
26 · Ordered permutations P(n, 2)
12. From 17 candidates, in how many ordered ways can a president and a vice-president be chosen?
17 · Ordered permutations P(n, 2)

12 questions · Seed 104737 · 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 20 candidates, in how many ordered ways can a president and a vice-president be chosen?
380
There are 20 choices for president and 19 remaining choices for vice-president: 20 × 19 = 380 ordered ways.
2. From 4 candidates, in how many ordered ways can a president and a vice-president be chosen?
12
There are 4 choices for president and 3 remaining choices for vice-president: 4 × 3 = 12 ordered ways.
3. 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.
4. From 14 candidates, in how many ordered ways can a president and a vice-president be chosen?
182
There are 14 choices for president and 13 remaining choices for vice-president: 14 × 13 = 182 ordered ways.
5. 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.
6. 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.
7. 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.
8. 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.
9. From 18 candidates, in how many ordered ways can a president and a vice-president be chosen?
306
There are 18 choices for president and 17 remaining choices for vice-president: 18 × 17 = 306 ordered ways.
10. From 30 candidates, in how many ordered ways can a president and a vice-president be chosen?
870
There are 30 choices for president and 29 remaining choices for vice-president: 30 × 29 = 870 ordered ways.
11. 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.
12. 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.

12 questions · Seed 104737 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 16-18

Ordered permutations P(n, 2)

Take your time. Show your thinking.

1. From 20 candidates, in how many ordered ways can a president and a vice-president be chosen?
20 · Ordered permutations P(n, 2)
2. From 4 candidates, in how many ordered ways can a president and a vice-president be chosen?
4 · Ordered permutations P(n, 2)
3. From 28 candidates, in how many ordered ways can a president and a vice-president be chosen?
28 · Ordered permutations P(n, 2)
4. From 14 candidates, in how many ordered ways can a president and a vice-president be chosen?
14 · Ordered permutations P(n, 2)
5. From 8 candidates, in how many ordered ways can a president and a vice-president be chosen?
8 · Ordered permutations P(n, 2)
6. From 10 candidates, in how many ordered ways can a president and a vice-president be chosen?
10 · Ordered permutations P(n, 2)
7. From 15 candidates, in how many ordered ways can a president and a vice-president be chosen?
15 · Ordered permutations P(n, 2)
8. From 5 candidates, in how many ordered ways can a president and a vice-president be chosen?
5 · Ordered permutations P(n, 2)
9. From 18 candidates, in how many ordered ways can a president and a vice-president be chosen?
18 · Ordered permutations P(n, 2)
10. From 30 candidates, in how many ordered ways can a president and a vice-president be chosen?
30 · Ordered permutations P(n, 2)
11. From 26 candidates, in how many ordered ways can a president and a vice-president be chosen?
26 · Ordered permutations P(n, 2)
12. From 17 candidates, in how many ordered ways can a president and a vice-president be chosen?
17 · Ordered permutations P(n, 2)

12 questions · Seed 104737 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 16-18

Ordered permutations P(n, 2)

Answers and reasoning. Review before teaching.

1. From 20 candidates, in how many ordered ways can a president and a vice-president be chosen?
380
There are 20 choices for president and 19 remaining choices for vice-president: 20 × 19 = 380 ordered ways.
2. From 4 candidates, in how many ordered ways can a president and a vice-president be chosen?
12
There are 4 choices for president and 3 remaining choices for vice-president: 4 × 3 = 12 ordered ways.
3. 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.
4. From 14 candidates, in how many ordered ways can a president and a vice-president be chosen?
182
There are 14 choices for president and 13 remaining choices for vice-president: 14 × 13 = 182 ordered ways.
5. 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.
6. 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.
7. 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.
8. 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.
9. From 18 candidates, in how many ordered ways can a president and a vice-president be chosen?
306
There are 18 choices for president and 17 remaining choices for vice-president: 18 × 17 = 306 ordered ways.
10. From 30 candidates, in how many ordered ways can a president and a vice-president be chosen?
870
There are 30 choices for president and 29 remaining choices for vice-president: 30 × 29 = 870 ordered ways.
11. 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.
12. 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.

12 questions · Seed 104737 · Age guidance, not curriculum certification