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 24 candidates, in how many ordered ways can a president and a vice-president be chosen?
24 · Ordered permutations P(n, 2)
3. From 19 candidates, in how many ordered ways can a president and a vice-president be chosen?
19 · Ordered permutations P(n, 2)
4. From 18 candidates, in how many ordered ways can a president and a vice-president be chosen?
18 · Ordered permutations P(n, 2)
5. From 7 candidates, in how many ordered ways can a president and a vice-president be chosen?
7 · Ordered permutations P(n, 2)
6. From 8 candidates, in how many ordered ways can a president and a vice-president be chosen?
8 · 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 4 candidates, in how many ordered ways can a president and a vice-president be chosen?
4 · Ordered permutations P(n, 2)
9. From 14 candidates, in how many ordered ways can a president and a vice-president be chosen?
14 · Ordered permutations P(n, 2)
10. From 6 candidates, in how many ordered ways can a president and a vice-president be chosen?
6 · Ordered permutations P(n, 2)
11. From 28 candidates, in how many ordered ways can a president and a vice-president be chosen?
28 · Ordered permutations P(n, 2)
12. From 29 candidates, in how many ordered ways can a president and a vice-president be chosen?
29 · Ordered permutations P(n, 2)

12 questions · Seed 104743 · 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 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 19 candidates, in how many ordered ways can a president and a vice-president be chosen?
342
There are 19 choices for president and 18 remaining choices for vice-president: 19 × 18 = 342 ordered ways.
4. 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.
5. 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.
6. 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.
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 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.
9. 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.
10. 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.
11. 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.
12. 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.

12 questions · Seed 104743 · 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 24 candidates, in how many ordered ways can a president and a vice-president be chosen?
24 · Ordered permutations P(n, 2)
3. From 19 candidates, in how many ordered ways can a president and a vice-president be chosen?
19 · Ordered permutations P(n, 2)
4. From 18 candidates, in how many ordered ways can a president and a vice-president be chosen?
18 · Ordered permutations P(n, 2)
5. From 7 candidates, in how many ordered ways can a president and a vice-president be chosen?
7 · Ordered permutations P(n, 2)
6. From 8 candidates, in how many ordered ways can a president and a vice-president be chosen?
8 · 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 4 candidates, in how many ordered ways can a president and a vice-president be chosen?
4 · Ordered permutations P(n, 2)
9. From 14 candidates, in how many ordered ways can a president and a vice-president be chosen?
14 · Ordered permutations P(n, 2)
10. From 6 candidates, in how many ordered ways can a president and a vice-president be chosen?
6 · Ordered permutations P(n, 2)
11. From 28 candidates, in how many ordered ways can a president and a vice-president be chosen?
28 · Ordered permutations P(n, 2)
12. From 29 candidates, in how many ordered ways can a president and a vice-president be chosen?
29 · Ordered permutations P(n, 2)

12 questions · Seed 104743 · 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 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 19 candidates, in how many ordered ways can a president and a vice-president be chosen?
342
There are 19 choices for president and 18 remaining choices for vice-president: 19 × 18 = 342 ordered ways.
4. 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.
5. 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.
6. 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.
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 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.
9. 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.
10. 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.
11. 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.
12. 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.

12 questions · Seed 104743 · Age guidance, not curriculum certification