Is there any reason why I could not solve the problem this way? Because I did and it turned out ok, but I don't always trust my own leaps of logic: Likewise you cannot take the number of possible favorable combination outcomes and divide that by the number of total possible permutation outcomes and get the correct probability. You cannot take the number of possible favorable permutation outcomes and divide that by the number of total possible combination outcomes and get the correct probability. You would not say that after moving 3 inches you are halfway to traveling 6 meters, even though 3/6 = ½. This is the same answer we got using permutations.Ĭonsider combinations and permutations to be different “units”. Our answer using combinations would be the number of favorable outcomes/the number of possible outcomes which would be 1/487,635. The number of possible combinations of 4 numbers taken out of 60 different numbers is 60!/((60-4)!*4!). Using combinations, there is only one (1) combination of numbers that gives us that favorable outcome (that one way, achu). Our answer using permutations would be the number of favorable outcomes/the number of possible outcomes which would be (4*3*2*1)/(60*59*58*57). The total number of different permutations of 4 numbers taken out of 60 different numbers is 60!/((60-4)!), which can be written as 60*59*58*57. Another way to say this is that there are 4! different ways to order the four numbers –or- there are 4! different permutations of the four numbers that give us the favorable outcome. Let us do it both ways, using the permutations first.Īs you mentioned, there a 4! ways of writing the four numbers. He could have taken the number of possible permutations with a favorable outcome and divided that by the total possible number of permutations –or-he could have taken the number of possible combinations with a favorable outcome and divided that by the total number of possible combinations (which is what he did). Sal could have solved this problem in two ways.
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