I have eleven books, of which I want to bring two to read on vacation. How many different pairs can I choose?
To choose a pair of books, I need to select two different books out of the eleven available. This is a combination problem, since the order of the books in the pair does not matter. I recall that the formula for the number of combinations of n objects taken r at a time is nCr = n!/(r!(n-r)!), where ! means factorial. In this case, n = 11 and r = 2, so I plug those values into the formula and simplify. I get 11C2 = 11!/(2!(11-2)!) = (11*10*9!)/(2*9!) = (11*10)/2 = 55. Therefore, there are 55 different pairs of books that I can choose. 