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Tuesday, May 21, 2013

Permutation Problems, 2

Category: Algebra, Statistics

"Published in Suisun City, California, USA"

A man bought three vanilla ice cream cones, two chocolate cones, four strawberry cones, and five butterscotch cones for his 14 children. In how many ways can he distribute  the cones among his children?

Solution:

The given word problem above is about permutations but it is a different type which is called a Distinguishable Permutation.  

If a set of n objects consists of k different kinds of objects with n1, objects of the first kind, n2 objects of the second kind, n3 objects of the third kind, and so on, where n1 + n2 + ......... + nk = n, then the number of distinguishable permutations of these objects is 


Now, let's go back to the given problem, if n = 14 children, n1 = 3 vanilla ice cream cones, n2 = 2 chocolate cones, n3 = 4 strawberry cones, and n4 = 5 butterscotch cones, then the number of ways to distribute the cones among to his children is