If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains ***.kastatic.org** and ***.kasandbox.org** are unblocked.

Main content

Current time:0:00Total duration:2:23

a club of nine people wants to choose a board of three officers president vice president and secretary assuming the officers are chosen at random what is the probability that the officers are marshal for president subida for Vice President and Robert for secretary so to think about the probability the probability of Marsha so let me write this president president is equal to Marsha so or vice president is equal to Savita Savita and secretary is equal to Robert Robert this is going to be this right here is one possible outcome one specific outcome so it's one outcome out of the total number of outcomes over the total number of possibilities total number of possibilities now what is the total number of possibilities well to think about that let's just think about the three positions let's just think about the three positions you have president you have vice president and you have secretary now let's just assume that we're going to fill the slot of president first we don't have to do president first but we're going to pick here so if we're just picking president first we haven't assigned anyone to any officers just yet so we have nine people to choose from so there are nine possibilities here now when we go to selecting our vice president we would have already assigned one person to the president so we only have eight people to pick from and when we assign our secretary we would have already assigned our president and vice president so we're only going to have seven people to pick from so the total permutations here or the total number of possibilities are the total number of ways to pick president vice president secretary from nine people is going to be 9 times 8 times 7 which is let's see 9 times 8 is 72 72 times 7 2 times 7 is 14 7 times 7 is 49 plus 1 is 50 so there's 504 possibilities possibilities so to answer the question the probability of Marshall being president subida being vice president Robert being secretary is one over the total number of possibilities which is one over 504 that's the probability