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 9 candidates, in how many ordered ways can a president and a vice-president be chosen?
9 · 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 29 candidates, in how many ordered ways can a president and a vice-president be chosen?
29 · Ordered permutations P(n, 2)
5. From 14 candidates, in how many ordered ways can a president and a vice-president be chosen?
14 · Ordered permutations P(n, 2)
6. From 13 candidates, in how many ordered ways can a president and a vice-president be chosen?
13 · Ordered permutations P(n, 2)
7. From 6 candidates, in how many ordered ways can a president and a vice-president be chosen?
6 · Ordered permutations P(n, 2)
8. From 10 candidates, in how many ordered ways can a president and a vice-president be chosen?
10 · 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 21 candidates, in how many ordered ways can a president and a vice-president be chosen?
21 · Ordered permutations P(n, 2)
11. From 16 candidates, in how many ordered ways can a president and a vice-president be chosen?
16 · Ordered permutations P(n, 2)
12. From 30 candidates, in how many ordered ways can a president and a vice-president be chosen?
30 · Ordered permutations P(n, 2)

12 questions · Seed 104749 · 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 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.
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 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.
5. 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.
6. 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.
7. 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.
8. 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.
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 21 candidates, in how many ordered ways can a president and a vice-president be chosen?
420
There are 21 choices for president and 20 remaining choices for vice-president: 21 × 20 = 420 ordered ways.
11. 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.
12. 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.

12 questions · Seed 104749 · 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 9 candidates, in how many ordered ways can a president and a vice-president be chosen?
9 · 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 29 candidates, in how many ordered ways can a president and a vice-president be chosen?
29 · Ordered permutations P(n, 2)
5. From 14 candidates, in how many ordered ways can a president and a vice-president be chosen?
14 · Ordered permutations P(n, 2)
6. From 13 candidates, in how many ordered ways can a president and a vice-president be chosen?
13 · Ordered permutations P(n, 2)
7. From 6 candidates, in how many ordered ways can a president and a vice-president be chosen?
6 · Ordered permutations P(n, 2)
8. From 10 candidates, in how many ordered ways can a president and a vice-president be chosen?
10 · 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 21 candidates, in how many ordered ways can a president and a vice-president be chosen?
21 · Ordered permutations P(n, 2)
11. From 16 candidates, in how many ordered ways can a president and a vice-president be chosen?
16 · Ordered permutations P(n, 2)
12. From 30 candidates, in how many ordered ways can a president and a vice-president be chosen?
30 · Ordered permutations P(n, 2)

12 questions · Seed 104749 · 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 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.
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 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.
5. 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.
6. 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.
7. 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.
8. 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.
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 21 candidates, in how many ordered ways can a president and a vice-president be chosen?
420
There are 21 choices for president and 20 remaining choices for vice-president: 21 × 20 = 420 ordered ways.
11. 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.
12. 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.

12 questions · Seed 104749 · Age guidance, not curriculum certification