Difference between revisions of "2008 UNCO Math Contest II Problems/Problem 10"
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== Solution == | == Solution == | ||
− | {{ | + | (a) <math>f(3,2)=15</math> |
+ | |||
+ | (b) <math>f(n,2)=(2n-1)!!</math> | ||
+ | |||
+ | (c) <math>f(2,3)=\binom{5}{2} ; f(3,3)=\binom{8}{2} \binom{5}{2} ;f(n,3)=\frac{(3n)!}{6^n \cdot n!} </math> | ||
== See Also == | == See Also == |
Revision as of 01:04, 13 January 2019
Problem
Let be the number of ways of splitting people into groups, each of size . As an example,
the people can be split into groups: and
Hence
(a) Compute and
(b) Conjecture a formula for
(c) Let be the number of ways of splitting into subsets of size . Compute and conjecture a formula for
Solution
(a)
(b)
(c)
See Also
2008 UNCO Math Contest II (Problems • Answer Key • Resources) | ||
Preceded by Problem 9 |
Followed by Last Question | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 | ||
All UNCO Math Contest Problems and Solutions |