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 21 candidates, in how many ordered ways can a president and a vice-president be chosen?
21 · 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 5 candidates, in how many ordered ways can a president and a vice-president be chosen?
5 · Ordered permutations P(n, 2)
4. From 4 candidates, in how many ordered ways can a president and a vice-president be chosen?
4 · Ordered permutations P(n, 2)
5. From 16 candidates, in how many ordered ways can a president and a vice-president be chosen?
16 · Ordered permutations P(n, 2)
6. From 6 candidates, in how many ordered ways can a president and a vice-president be chosen?
6 · Ordered permutations P(n, 2)
7. From 7 candidates, in how many ordered ways can a president and a vice-president be chosen?
7 · Ordered permutations P(n, 2)
8. From 30 candidates, in how many ordered ways can a president and a vice-president be chosen?
30 · Ordered permutations P(n, 2)
9. From 13 candidates, in how many ordered ways can a president and a vice-president be chosen?
13 · Ordered permutations P(n, 2)
10. From 27 candidates, in how many ordered ways can a president and a vice-president be chosen?
27 · Ordered permutations P(n, 2)
11. From 8 candidates, in how many ordered ways can a president and a vice-president be chosen?
8 · Ordered permutations P(n, 2)
12. From 20 candidates, in how many ordered ways can a president and a vice-president be chosen?
20 · Ordered permutations P(n, 2)

12 questions · Seed 104736 · 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 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.
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 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.
4. 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.
5. 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.
6. 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.
7. 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.
8. 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.
9. 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.
10. From 27 candidates, in how many ordered ways can a president and a vice-president be chosen?
702
There are 27 choices for president and 26 remaining choices for vice-president: 27 × 26 = 702 ordered ways.
11. 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.
12. From 20 candidates, in how many ordered ways can a president and a vice-president be chosen?
380
There are 20 choices for president and 19 remaining choices for vice-president: 20 × 19 = 380 ordered ways.

12 questions · Seed 104736 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 16-18

Ordered permutations P(n, 2)

Take your time. Show your thinking.

1. From 21 candidates, in how many ordered ways can a president and a vice-president be chosen?
21 · 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 5 candidates, in how many ordered ways can a president and a vice-president be chosen?
5 · Ordered permutations P(n, 2)
4. From 4 candidates, in how many ordered ways can a president and a vice-president be chosen?
4 · Ordered permutations P(n, 2)
5. From 16 candidates, in how many ordered ways can a president and a vice-president be chosen?
16 · Ordered permutations P(n, 2)
6. From 6 candidates, in how many ordered ways can a president and a vice-president be chosen?
6 · Ordered permutations P(n, 2)
7. From 7 candidates, in how many ordered ways can a president and a vice-president be chosen?
7 · Ordered permutations P(n, 2)
8. From 30 candidates, in how many ordered ways can a president and a vice-president be chosen?
30 · Ordered permutations P(n, 2)
9. From 13 candidates, in how many ordered ways can a president and a vice-president be chosen?
13 · Ordered permutations P(n, 2)
10. From 27 candidates, in how many ordered ways can a president and a vice-president be chosen?
27 · Ordered permutations P(n, 2)
11. From 8 candidates, in how many ordered ways can a president and a vice-president be chosen?
8 · Ordered permutations P(n, 2)
12. From 20 candidates, in how many ordered ways can a president and a vice-president be chosen?
20 · Ordered permutations P(n, 2)

12 questions · Seed 104736 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 16-18

Ordered permutations P(n, 2)

Answers and reasoning. Review before teaching.

1. 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.
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 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.
4. 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.
5. 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.
6. 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.
7. 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.
8. 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.
9. 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.
10. From 27 candidates, in how many ordered ways can a president and a vice-president be chosen?
702
There are 27 choices for president and 26 remaining choices for vice-president: 27 × 26 = 702 ordered ways.
11. 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.
12. From 20 candidates, in how many ordered ways can a president and a vice-president be chosen?
380
There are 20 choices for president and 19 remaining choices for vice-president: 20 × 19 = 380 ordered ways.

12 questions · Seed 104736 · Age guidance, not curriculum certification