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 11 candidates, in how many ordered ways can a president and a vice-president be chosen?
11 · Ordered permutations P(n, 2)
2. From 24 candidates, in how many ordered ways can a president and a vice-president be chosen?
24 · Ordered permutations P(n, 2)
3. From 13 candidates, in how many ordered ways can a president and a vice-president be chosen?
13 · 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 12 candidates, in how many ordered ways can a president and a vice-president be chosen?
12 · Ordered permutations P(n, 2)
6. From 28 candidates, in how many ordered ways can a president and a vice-president be chosen?
28 · Ordered permutations P(n, 2)
7. From 29 candidates, in how many ordered ways can a president and a vice-president be chosen?
29 · Ordered permutations P(n, 2)
8. From 14 candidates, in how many ordered ways can a president and a vice-president be chosen?
14 · 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 21 candidates, in how many ordered ways can a president and a vice-president be chosen?
21 · Ordered permutations P(n, 2)
11. From 25 candidates, in how many ordered ways can a president and a vice-president be chosen?
25 · 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 44 · 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 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.
2. 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.
3. 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.
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 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.
6. 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.
7. 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.
8. 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.
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 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 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. 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 44 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 16-18

Ordered permutations P(n, 2)

Take your time. Show your thinking.

1. From 11 candidates, in how many ordered ways can a president and a vice-president be chosen?
11 · Ordered permutations P(n, 2)
2. From 24 candidates, in how many ordered ways can a president and a vice-president be chosen?
24 · Ordered permutations P(n, 2)
3. From 13 candidates, in how many ordered ways can a president and a vice-president be chosen?
13 · 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 12 candidates, in how many ordered ways can a president and a vice-president be chosen?
12 · Ordered permutations P(n, 2)
6. From 28 candidates, in how many ordered ways can a president and a vice-president be chosen?
28 · Ordered permutations P(n, 2)
7. From 29 candidates, in how many ordered ways can a president and a vice-president be chosen?
29 · Ordered permutations P(n, 2)
8. From 14 candidates, in how many ordered ways can a president and a vice-president be chosen?
14 · 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 21 candidates, in how many ordered ways can a president and a vice-president be chosen?
21 · Ordered permutations P(n, 2)
11. From 25 candidates, in how many ordered ways can a president and a vice-president be chosen?
25 · 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 44 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 16-18

Ordered permutations P(n, 2)

Answers and reasoning. Review before teaching.

1. 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.
2. 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.
3. 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.
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 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.
6. 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.
7. 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.
8. 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.
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 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 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. 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 44 · Age guidance, not curriculum certification