Question 245890: A class contains 13 boys and 15girls .how many different ways can the class pick a president,vice-president and secretary?
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
That would depend on whether, as your introductory sentence would imply, that you are asking how many gender permutations are possible or if you want the number of permutations of 28 individual people.
If you are only concerned with gender, there are two ways (boy or girl) to select the president. For each of these two ways there are two ways to select the vice-president, for a total of four ways. And finally, for each of these four ways there are two ways to select the secretary for a grand total of 8 ways.
On the other hand, if you are concerned with permutations of individuals, then there are 28 ways to select the president, then for each of those ways, there are 27 ways to select the vice-president (one less because you would presume that the president and vice-president need to be two different people), so 28 times 27. Then for each of those ways there are 26 ways to select the secretary.
So:
!}\ =\ 28\ \times\ 27\ \times\ 26)
John
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