Organized Counting

Permutations and Combinations

Jones is the Chairman of a committee. In how many ways can a committee of 5 be chosen from 10 people given that

Jones must be one of them?

1 2 3 4

87%

6%3%3%

1. 1262. 2523. 4954. 3024

A password consists of four different letters of the alphabet. How many different possible passwords are

there?

1 2 3 4

0%

71%

26%

3%

1. 4^262. 4569763. 149504. 358800

A password consists of two letters of the alphabet followed by three digits chosen from 0 to 9. Repeats are allowed. How many different

possible passwords are there?

1 2 3 4

3% 0%

94%

3%

1. 4928042. 6500003. 6760004. 1757600

An encyclopedia has eight volumes. In how many ways can the eight volumes

be replaced on the shelf?

1 2 3 4

0% 0%

90%

10%

1. 82. 50403. 403204. 8^8

Assuming that any arrangement of letters forms a 'word', how many 'words' of any length can be

formed from the letters of the word SQUARE?(No repeating of letters)

1 2 3 4

0% 0%

77%

23%

1. 822. 7203. 19564. 9331

A restaurant offers 5 choices of appetizer, 10 choices of main meal and 4 choices of dessert. A customer can choose to eat just

one course, or two different courses, or all three courses. Assuming all choices are available, how many different possible

meals does the restaurant offer?

1 2 3 4

23%

16%

39%

23%

1. 3292. 3103. 2004. 19

How many permutations of 3 different digits are there, chosen from the ten digits

0 to 9 inclusive?

1 2 3 4

0%

90%

3%6%

1. 842. 1203. 5044. 720

How many permutations of 3 different digits are there, chosen from the ten digits

0 to 9 inclusive?

1 2 3 4

0%

100%

0%0%

1. 842. 1203. 5044. 720

How many permutations of 4 different letters are there, chosen from the twenty

six letters of the alphabet (repetition is not allowed)?

1 2 3 4

0% 0%

100%

0%

1. 149502. 237513. 3588004. 456976

How many different committees of 5 people can be chosen from 10 people?

1 2 3 4

87%

0%

13%3%

1. 2522. 20023. 302404. 100000

Fastest Responders (in seconds)9.64 Maggie Haun17.17 Fiona Corbett17.44 Tony Li17.64 Nick Whitty19.7 Alex Watson

Participant Scores10 Shabana Jamani10 Mark Rankin9 Maggie Haun9 Fiona Corbett9 Tony Li9 Nick Whitty9 Jen Antonishen9 Lucas Di Lorio9 Clare Johnson9 Jialing Wu