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 30 candidates, in how many ordered ways can a president and a vice-president be chosen?
30 · Ordered permutations P(n, 2)
2. From 22 candidates, in how many ordered ways can a president and a vice-president be chosen?
22 · Ordered permutations P(n, 2)
3. From 25 candidates, in how many ordered ways can a president and a vice-president be chosen?
25 · 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 5 candidates, in how many ordered ways can a president and a vice-president be chosen?
5 · Ordered permutations P(n, 2)
7. From 28 candidates, in how many ordered ways can a president and a vice-president be chosen?
28 · Ordered permutations P(n, 2)
8. From 16 candidates, in how many ordered ways can a president and a vice-president be chosen?
16 · Ordered permutations P(n, 2)
9. From 11 candidates, in how many ordered ways can a president and a vice-president be chosen?
11 · Ordered permutations P(n, 2)
10. From 7 candidates, in how many ordered ways can a president and a vice-president be chosen?
7 · 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 14 candidates, in how many ordered ways can a president and a vice-president be chosen?
14 · Ordered permutations P(n, 2)

12 questions · Seed 104738 · 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 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.
2. 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.
3. 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.
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 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.
7. 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.
8. From 16 candidates, in how many ordered ways can a president and a vice-president be chosen?
240
There are 16 choices for president and 15 remaining choices for vice-president: 16 × 15 = 240 ordered ways.
9. From 11 candidates, in how many ordered ways can a president and a vice-president be chosen?
110
There are 11 choices for president and 10 remaining choices for vice-president: 11 × 10 = 110 ordered ways.
10. 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.
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 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.

12 questions · Seed 104738 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 16-18

Ordered permutations P(n, 2)

Take your time. Show your thinking.

1. From 30 candidates, in how many ordered ways can a president and a vice-president be chosen?
30 · Ordered permutations P(n, 2)
2. From 22 candidates, in how many ordered ways can a president and a vice-president be chosen?
22 · Ordered permutations P(n, 2)
3. From 25 candidates, in how many ordered ways can a president and a vice-president be chosen?
25 · 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 5 candidates, in how many ordered ways can a president and a vice-president be chosen?
5 · Ordered permutations P(n, 2)
7. From 28 candidates, in how many ordered ways can a president and a vice-president be chosen?
28 · Ordered permutations P(n, 2)
8. From 16 candidates, in how many ordered ways can a president and a vice-president be chosen?
16 · Ordered permutations P(n, 2)
9. From 11 candidates, in how many ordered ways can a president and a vice-president be chosen?
11 · Ordered permutations P(n, 2)
10. From 7 candidates, in how many ordered ways can a president and a vice-president be chosen?
7 · 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 14 candidates, in how many ordered ways can a president and a vice-president be chosen?
14 · Ordered permutations P(n, 2)

12 questions · Seed 104738 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 16-18

Ordered permutations P(n, 2)

Answers and reasoning. Review before teaching.

1. 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.
2. 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.
3. 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.
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 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.
7. 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.
8. From 16 candidates, in how many ordered ways can a president and a vice-president be chosen?
240
There are 16 choices for president and 15 remaining choices for vice-president: 16 × 15 = 240 ordered ways.
9. From 11 candidates, in how many ordered ways can a president and a vice-president be chosen?
110
There are 11 choices for president and 10 remaining choices for vice-president: 11 × 10 = 110 ordered ways.
10. 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.
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 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.

12 questions · Seed 104738 · Age guidance, not curriculum certification