# not a permutation? then how?

• March 15th 2008, 10:29 PM
dreamer1963
not a permutation? then how?
There are two small towns, Greenville and Yellowville. Greenville contains 20 houses and Yellowville contains 15 houses. The state safety inspector is asked to randomly inspect 5 houses in Greenville and 7 houses in Yellowville. In how many ways can this be done (Hint: this is not a permutation)?
• March 16th 2008, 01:09 AM
Moo
Hello,

This is a combination.

You "take" 5 elements among 20 elements (the houses).

Combination - Wikipedia, the free encyclopedia
• March 16th 2008, 01:28 AM
dreamer1963
thank you. I think I am making it more difficult than it really is.
• March 16th 2008, 01:50 AM
mr fantastic
Quote:

Originally Posted by dreamer1963
There are two small towns, Greenville and Yellowville. Greenville contains 20 houses and Yellowville contains 15 houses. The state safety inspector is asked to randomly inspect 5 houses in Greenville and 7 houses in Yellowville. In how many ways can this be done (Hint: this is not a permutation)?

${20 \choose 5} \times {15 \choose 7}$