Factors!
Probability
Level
3
How many different ways can you arrange elements from {1,1,1,1,2,2,5,5} into the form: {a,b,c,d}, assuming order doesn't matter? i.e. {1,1,2,2} and {1,2,1,2} are the same thing.
The answer is 9.
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1 solution
Notice that 1,1,1,1,2,2,5,5 are prime factors of 100. Also notice that any factor of 100 can be represented by multiplying any four of these numbers together (because there are four 1's). Thus, this question can be solved by finding the number of factors of 100. This can be done by representing 100 as prime factors like so: (2^2)(5^2). Add 1 to each exponent and multiply these values together in order to find the number of factors: (2+1)*(2+1)=9 (this is a property of all natural numbers). Therefore, the answer is 9.