1. How many permutation of 5 different digits can be arrange from the numbers 0 to 20
There are 21 elements in this set
{0,1,2,3,4,5,6,7,8,9,10,1,12,13,14,15,16,17,18,19,20}
P(21,5) = 21·20·19·18·17 = 2441880
2. How many permutation of 3 different letters can be arrange from the word “NOTEBOOK” (repetition is not allowed)
That's the set {N,O,T,E,B,K} which contains 6 elements.
P(6,3) = 6·5·4 = 120.
3. A password consists of 4 characters, the two characters is made of alpha characters from A-E and the other two characters is made from F-G. How many arrangement of character can be made?
Choose two from A-E in C(5,2)=10 ways, and from F-G in C(2,2) = 1 way. That's
10 ways.
4. How many words can be made from the word “KEYBOARD” with any length?
1-letter words = P(8,1) = 8
2-letter words = P(8,2) = 8·7 = 56
3-letter words = P(8,3) = 8·7·6 = 336
4-letter words = P(8,4) = 8·7·6·5 = 1680
5-letter words = P(8,5) = 8·7·6·5·4 = 6720
6-letter words = P(8,6) = 8·7·6·5·4·3 = 20160
7-letter words = P(8,7) = 8·7·6·5·4·3·2 = 40320
8-letter words = P(8,8) = 8·7·6·5·4·3·2·1 = 40320
Add those up = 109600
Edwin
