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The number of permutations of 5 things taken 2 at a time is 20?
Not quite. Number of combinations is 20, number of permutations is 10. Any 2 from 5 is 10 but in any order doubles this.
How many three digit numbers can you write using the digits 1 2 3 4 5 without repeating?
The first digit can be any one of 5 choices. For each of those, the second digit can be any one of 4 choices. For each of those, the third digit can be any one of 3 choices. So the total number of permutations without repetition is 5 x 4 x 3 = 60.
When two dice are rolled what is the probability that both will not be the same number?
The are 36 permutations of two dice. Of these, 6 permutations have the two dice with the same number, specifically 1+1, 2+2, 3+3, 4+4, 5+5, and 6+6. The probability, then, that two dice rolled will not have the same number is 30 in 36, or 5 in 6, or about 0.8333.
Suppose you find six articles related to the topic of your research paper In how many ways can you choose four articles to read?
6*5*4*3 = 360 ways. http://en.wikipedia.org/wiki/Permutations
How many codes can I make out of 01234?
If you are looking to create codes using the digits 0, 1, 2, 3, and 4 without repetition, you would be creating permutations. The number of permutations of n items taken r at a time is given by the formula P(n,r) = n! / (n-r)!. In this case, you have 5 digits to choose from (n=5) and you want to create a code with all 5 digits (r=5). Therefore, the number of codes you can make is 5! / (5-5)! = 5! / 0! = 5! = 5 x 4 x 3 x 2 x 1 = 120.
