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.
