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 24 candidates, in how many ordered ways can a president and a vice-president be chosen?
24 · Ordered permutations P(n, 2)
2. From 7 candidates, in how many ordered ways can a president and a vice-president be chosen?
7 · Ordered permutations P(n, 2)
3. From 4 candidates, in how many ordered ways can a president and a vice-president be chosen?
4 · Ordered permutations P(n, 2)
4. From 23 candidates, in how many ordered ways can a president and a vice-president be chosen?
23 · Ordered permutations P(n, 2)
5. From 9 candidates, in how many ordered ways can a president and a vice-president be chosen?
9 · Ordered permutations P(n, 2)
6. From 15 candidates, in how many ordered ways can a president and a vice-president be chosen?
15 · Ordered permutations P(n, 2)
7. From 13 candidates, in how many ordered ways can a president and a vice-president be chosen?
13 · 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 27 candidates, in how many ordered ways can a president and a vice-president be chosen?
27 · 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 12 candidates, in how many ordered ways can a president and a vice-president be chosen?
12 · Ordered permutations P(n, 2)
12. From 20 candidates, in how many ordered ways can a president and a vice-president be chosen?
20 · Ordered permutations P(n, 2)

12 questions · Seed 43 · 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 24 candidates, in how many ordered ways can a president and a vice-president be chosen?
552
There are 24 choices for president and 23 remaining choices for vice-president: 24 × 23 = 552 ordered ways.
2. From 7 candidates, in how many ordered ways can a president and a vice-president be chosen?
42
There are 7 choices for president and 6 remaining choices for vice-president: 7 × 6 = 42 ordered ways.
3. 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.
4. 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.
5. From 9 candidates, in how many ordered ways can a president and a vice-president be chosen?
72
There are 9 choices for president and 8 remaining choices for vice-president: 9 × 8 = 72 ordered ways.
6. 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.
7. From 13 candidates, in how many ordered ways can a president and a vice-president be chosen?
156
There are 13 choices for president and 12 remaining choices for vice-president: 13 × 12 = 156 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 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.
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 12 candidates, in how many ordered ways can a president and a vice-president be chosen?
132
There are 12 choices for president and 11 remaining choices for vice-president: 12 × 11 = 132 ordered ways.
12. 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.

12 questions · Seed 43 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 16-18

Ordered permutations P(n, 2)

Take your time. Show your thinking.

1. From 24 candidates, in how many ordered ways can a president and a vice-president be chosen?
24 · Ordered permutations P(n, 2)
2. From 7 candidates, in how many ordered ways can a president and a vice-president be chosen?
7 · Ordered permutations P(n, 2)
3. From 4 candidates, in how many ordered ways can a president and a vice-president be chosen?
4 · Ordered permutations P(n, 2)
4. From 23 candidates, in how many ordered ways can a president and a vice-president be chosen?
23 · Ordered permutations P(n, 2)
5. From 9 candidates, in how many ordered ways can a president and a vice-president be chosen?
9 · Ordered permutations P(n, 2)
6. From 15 candidates, in how many ordered ways can a president and a vice-president be chosen?
15 · Ordered permutations P(n, 2)
7. From 13 candidates, in how many ordered ways can a president and a vice-president be chosen?
13 · 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 27 candidates, in how many ordered ways can a president and a vice-president be chosen?
27 · 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 12 candidates, in how many ordered ways can a president and a vice-president be chosen?
12 · Ordered permutations P(n, 2)
12. From 20 candidates, in how many ordered ways can a president and a vice-president be chosen?
20 · Ordered permutations P(n, 2)

12 questions · Seed 43 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 16-18

Ordered permutations P(n, 2)

Answers and reasoning. Review before teaching.

1. From 24 candidates, in how many ordered ways can a president and a vice-president be chosen?
552
There are 24 choices for president and 23 remaining choices for vice-president: 24 × 23 = 552 ordered ways.
2. From 7 candidates, in how many ordered ways can a president and a vice-president be chosen?
42
There are 7 choices for president and 6 remaining choices for vice-president: 7 × 6 = 42 ordered ways.
3. 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.
4. 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.
5. From 9 candidates, in how many ordered ways can a president and a vice-president be chosen?
72
There are 9 choices for president and 8 remaining choices for vice-president: 9 × 8 = 72 ordered ways.
6. 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.
7. From 13 candidates, in how many ordered ways can a president and a vice-president be chosen?
156
There are 13 choices for president and 12 remaining choices for vice-president: 13 × 12 = 156 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 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.
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 12 candidates, in how many ordered ways can a president and a vice-president be chosen?
132
There are 12 choices for president and 11 remaining choices for vice-president: 12 × 11 = 132 ordered ways.
12. 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.

12 questions · Seed 43 · Age guidance, not curriculum certification