2015 UNCO Math Contest II Problems/Problem 8


A garden urn contains $18$ colored beetles: $6$ red beetles, numbered from $1$ to $6$, and $12$ yellow beetles, numbered from $1$ to $12$. Beetles wander out of the urn in random order, one at a time, without any going back in. What is the probability that the sequence of numbers on the first four beetles to wander out is steadily increasing, that is, that the number on each beetle to wander out is larger than the number on the beetle before and that no number is repeated? Give your answer as a fraction in lowest terms. You may leave the numerator and denominator in a factored form.


$\frac{157}{(18 \times 17 \times 16)} = \frac{157}{4896}$

See also

2015 UNCO Math Contest II (ProblemsAnswer KeyResources)
Preceded by
Problem 7
Followed by
Problem 9
1 2 3 4 5 6 7 8 9 10
All UNCO Math Contest Problems and Solutions