2005 PMWC Problems/Problem I11
Problem
There are 4 men: A, B, C and D. Each has a son. The four sons are asked to enter a dark room. Then A, B, C and D enter the dark room, and each of them walks out with just one child. If none of them comes out with his own son, in how many ways can this happen?
Solution
This is just a derangement problem (sending the set to another set such that none of the original elements are in the same place). The formula is:
When , we get:
See also
2005 PMWC (Problems) | ||
Preceded by Problem I10 |
Followed by Problem I12 | |
I: 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 T: 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 |