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 15 candidates, in how many ordered ways can a president and a vice-president be chosen?
15 · Ordered permutations P(n, 2)
2. From 12 candidates, in how many ordered ways can a president and a vice-president be chosen?
12 · Ordered permutations P(n, 2)
3. From 10 candidates, in how many ordered ways can a president and a vice-president be chosen?
10 · Ordered permutations P(n, 2)
4. From 5 candidates, in how many ordered ways can a president and a vice-president be chosen?
5 · Ordered permutations P(n, 2)
5. From 29 candidates, in how many ordered ways can a president and a vice-president be chosen?
29 · Ordered permutations P(n, 2)
6. From 4 candidates, in how many ordered ways can a president and a vice-president be chosen?
4 · Ordered permutations P(n, 2)
7. From 23 candidates, in how many ordered ways can a president and a vice-president be chosen?
23 · Ordered permutations P(n, 2)
8. From 8 candidates, in how many ordered ways can a president and a vice-president be chosen?
8 · Ordered permutations P(n, 2)
9. From 7 candidates, in how many ordered ways can a president and a vice-president be chosen?
7 · Ordered permutations P(n, 2)
10. From 16 candidates, in how many ordered ways can a president and a vice-president be chosen?
16 · Ordered permutations P(n, 2)
11. From 24 candidates, in how many ordered ways can a president and a vice-president be chosen?
24 · 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 42 · 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 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.
2. 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.
3. 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.
4. 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.
5. From 29 candidates, in how many ordered ways can a president and a vice-president be chosen?
812
There are 29 choices for president and 28 remaining choices for vice-president: 29 × 28 = 812 ordered ways.
6. 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.
7. 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.
8. 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.
9. 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.
10. 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.
11. 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.
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 42 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 16-18

Ordered permutations P(n, 2)

Take your time. Show your thinking.

1. From 15 candidates, in how many ordered ways can a president and a vice-president be chosen?
15 · Ordered permutations P(n, 2)
2. From 12 candidates, in how many ordered ways can a president and a vice-president be chosen?
12 · Ordered permutations P(n, 2)
3. From 10 candidates, in how many ordered ways can a president and a vice-president be chosen?
10 · Ordered permutations P(n, 2)
4. From 5 candidates, in how many ordered ways can a president and a vice-president be chosen?
5 · Ordered permutations P(n, 2)
5. From 29 candidates, in how many ordered ways can a president and a vice-president be chosen?
29 · Ordered permutations P(n, 2)
6. From 4 candidates, in how many ordered ways can a president and a vice-president be chosen?
4 · Ordered permutations P(n, 2)
7. From 23 candidates, in how many ordered ways can a president and a vice-president be chosen?
23 · Ordered permutations P(n, 2)
8. From 8 candidates, in how many ordered ways can a president and a vice-president be chosen?
8 · Ordered permutations P(n, 2)
9. From 7 candidates, in how many ordered ways can a president and a vice-president be chosen?
7 · Ordered permutations P(n, 2)
10. From 16 candidates, in how many ordered ways can a president and a vice-president be chosen?
16 · Ordered permutations P(n, 2)
11. From 24 candidates, in how many ordered ways can a president and a vice-president be chosen?
24 · 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 42 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 16-18

Ordered permutations P(n, 2)

Answers and reasoning. Review before teaching.

1. 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.
2. 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.
3. 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.
4. 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.
5. From 29 candidates, in how many ordered ways can a president and a vice-president be chosen?
812
There are 29 choices for president and 28 remaining choices for vice-president: 29 × 28 = 812 ordered ways.
6. 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.
7. 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.
8. 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.
9. 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.
10. 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.
11. 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.
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 42 · Age guidance, not curriculum certification