



 
Jon, The number of ways to choose a collection of k distinguishable objects from a collection of n distinguishable objects is denoted by the symbol C(n,k), and read as "n choose k". You are looking for C(36, 3), that is, 36 choose 3. To find a formula for C(n, k), when 0 <= k <= n, count the number of arrangements of k out of n distinguishable objects in a line, where repetitions are not allowed, in two different ways and equate the answers. The two expressions we get are equal because they represent the same number. First, imagine choosing the k objects and then arranging them in a line. There are C(n,k) ways to choose the k objects, and k! ways to arrange them in a line. Therefore, the number of such lines is C(n,k)k!. Second, count the number of such lines directly. There are n choices for the object on the left end of the line, then n1 choices for the one next to it, then n2 choices for the next one, and so on until, finally, there are n(k1) choices for the last object in the line. Thus, the number of such lines is n(n1)(n2)...(n(k1)) = n!/(nk)!. Therefore, C(n,k)k! = n!/(nk)!, so that C(n,k)=n!/(k!(nk)!). Victoria
 


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