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 02:04, 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 | ||
