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 10 candidates, in how many ordered ways can a president and a vice-president be chosen?
10 · Ordered permutations P(n, 2)
2. From 7 candidates, in how many ordered ways can a president and a vice-president be chosen?
7 · Ordered permutations P(n, 2)
3. From 27 candidates, in how many ordered ways can a president and a vice-president be chosen?
27 · Ordered permutations P(n, 2)
4. From 19 candidates, in how many ordered ways can a president and a vice-president be chosen?
19 · Ordered permutations P(n, 2)
5. From 20 candidates, in how many ordered ways can a president and a vice-president be chosen?
20 · Ordered permutations P(n, 2)
6. From 29 candidates, in how many ordered ways can a president and a vice-president be chosen?
29 · Ordered permutations P(n, 2)
7. From 9 candidates, in how many ordered ways can a president and a vice-president be chosen?
9 · Ordered permutations P(n, 2)
8. From 17 candidates, in how many ordered ways can a president and a vice-president be chosen?
17 · 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 12 candidates, in how many ordered ways can a president and a vice-president be chosen?
12 · Ordered permutations P(n, 2)
11. From 22 candidates, in how many ordered ways can a president and a vice-president be chosen?
22 · Ordered permutations P(n, 2)
12. From 4 candidates, in how many ordered ways can a president and a vice-president be chosen?
4 · Ordered permutations P(n, 2)

12 questions · Seed 104735 · 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 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.
2. 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.
3. 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.
4. 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.
5. 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.
6. 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.
7. 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.
8. 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.
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 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.
11. 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.
12. 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.

12 questions · Seed 104735 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 16-18

Ordered permutations P(n, 2)

Take your time. Show your thinking.

1. From 10 candidates, in how many ordered ways can a president and a vice-president be chosen?
10 · Ordered permutations P(n, 2)
2. From 7 candidates, in how many ordered ways can a president and a vice-president be chosen?
7 · Ordered permutations P(n, 2)
3. From 27 candidates, in how many ordered ways can a president and a vice-president be chosen?
27 · Ordered permutations P(n, 2)
4. From 19 candidates, in how many ordered ways can a president and a vice-president be chosen?
19 · Ordered permutations P(n, 2)
5. From 20 candidates, in how many ordered ways can a president and a vice-president be chosen?
20 · Ordered permutations P(n, 2)
6. From 29 candidates, in how many ordered ways can a president and a vice-president be chosen?
29 · Ordered permutations P(n, 2)
7. From 9 candidates, in how many ordered ways can a president and a vice-president be chosen?
9 · Ordered permutations P(n, 2)
8. From 17 candidates, in how many ordered ways can a president and a vice-president be chosen?
17 · 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 12 candidates, in how many ordered ways can a president and a vice-president be chosen?
12 · Ordered permutations P(n, 2)
11. From 22 candidates, in how many ordered ways can a president and a vice-president be chosen?
22 · Ordered permutations P(n, 2)
12. From 4 candidates, in how many ordered ways can a president and a vice-president be chosen?
4 · Ordered permutations P(n, 2)

12 questions · Seed 104735 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 16-18

Ordered permutations P(n, 2)

Answers and reasoning. Review before teaching.

1. 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.
2. 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.
3. 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.
4. 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.
5. 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.
6. 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.
7. 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.
8. 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.
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 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.
11. 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.
12. 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.

12 questions · Seed 104735 · Age guidance, not curriculum certification