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 18 candidates, in how many ordered ways can a president and a vice-president be chosen?
18 · Ordered permutations P(n, 2)
2. From 23 candidates, in how many ordered ways can a president and a vice-president be chosen?
23 · Ordered permutations P(n, 2)
3. From 22 candidates, in how many ordered ways can a president and a vice-president be chosen?
22 · Ordered permutations P(n, 2)
4. From 20 candidates, in how many ordered ways can a president and a vice-president be chosen?
20 · Ordered permutations P(n, 2)
5. From 5 candidates, in how many ordered ways can a president and a vice-president be chosen?
5 · Ordered permutations P(n, 2)
6. From 26 candidates, in how many ordered ways can a president and a vice-president be chosen?
26 · Ordered permutations P(n, 2)
7. From 21 candidates, in how many ordered ways can a president and a vice-president be chosen?
21 · 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 12 candidates, in how many ordered ways can a president and a vice-president be chosen?
12 · 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 14 candidates, in how many ordered ways can a president and a vice-president be chosen?
14 · 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 104742 · 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 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.
2. 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.
3. From 22 candidates, in how many ordered ways can a president and a vice-president be chosen?
462
There are 22 choices for president and 21 remaining choices for vice-president: 22 × 21 = 462 ordered ways.
4. 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.
5. 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.
6. From 26 candidates, in how many ordered ways can a president and a vice-president be chosen?
650
There are 26 choices for president and 25 remaining choices for vice-president: 26 × 25 = 650 ordered ways.
7. 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.
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 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.
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 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.
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 104742 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 16-18

Ordered permutations P(n, 2)

Take your time. Show your thinking.

1. From 18 candidates, in how many ordered ways can a president and a vice-president be chosen?
18 · Ordered permutations P(n, 2)
2. From 23 candidates, in how many ordered ways can a president and a vice-president be chosen?
23 · Ordered permutations P(n, 2)
3. From 22 candidates, in how many ordered ways can a president and a vice-president be chosen?
22 · Ordered permutations P(n, 2)
4. From 20 candidates, in how many ordered ways can a president and a vice-president be chosen?
20 · Ordered permutations P(n, 2)
5. From 5 candidates, in how many ordered ways can a president and a vice-president be chosen?
5 · Ordered permutations P(n, 2)
6. From 26 candidates, in how many ordered ways can a president and a vice-president be chosen?
26 · Ordered permutations P(n, 2)
7. From 21 candidates, in how many ordered ways can a president and a vice-president be chosen?
21 · 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 12 candidates, in how many ordered ways can a president and a vice-president be chosen?
12 · 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 14 candidates, in how many ordered ways can a president and a vice-president be chosen?
14 · 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 104742 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 16-18

Ordered permutations P(n, 2)

Answers and reasoning. Review before teaching.

1. 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.
2. 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.
3. From 22 candidates, in how many ordered ways can a president and a vice-president be chosen?
462
There are 22 choices for president and 21 remaining choices for vice-president: 22 × 21 = 462 ordered ways.
4. 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.
5. 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.
6. From 26 candidates, in how many ordered ways can a president and a vice-president be chosen?
650
There are 26 choices for president and 25 remaining choices for vice-president: 26 × 25 = 650 ordered ways.
7. 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.
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 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.
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 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.
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 104742 · Age guidance, not curriculum certification