Monday

September 22, 2014

September 22, 2014

Posted by **Andy** on Friday, June 29, 2012 at 8:41pm.

- math -
**David Q/R**, Sunday, July 1, 2012 at 4:37pmThis sounds a bit badly worded to me, since strictly speaking there is NO way that eight cars can fit into two spaces that between them can accommodate at most five cars. However I assume that the question is intended to be "In how many ways can exactly five out of eight cars be parked in two big spaces, one of which will take three and the other of which will take two?".

However... if that's right, then there's another question to answer first, which is "Do we distinguish between the six different configurations that any three cars can occupy in the big space, or between the two different configurations that any two cars can occupy in the small space?".

If we DON'T distinguish between them, then I think the answer would be 8!/(3! x 5!) x 5!/(2! x 3!) = 42 x 10 = 420. The reason for that is that we need to calculate the number of ways in which three cars out of eight can occupy the larger space {8!/(3! x 5!)}, and that needs to be multiplied by the number of ways in which two of the remaining five cars can occupy the smaller space (5!/(2! x 3!).

If we DO distinguish between them, then I think the answer would be (8!/3!) x (5!/2!) = (8.7.6.5.4).(5.4.3) = 403,200.

Having said that, I'm not actually certain about either answer, so please do check them.

**Answer this Question**

**Related Questions**

MATH - A parking lot has 5 spots remaining and 5 different cars in line waiting ...

Math - Yesterday, a parking lot had 60 cars parked in it. Of the cars parked in ...

algebra - a new parking lothas spaces for 450 cars. the ratio of spaces for ...

Math probability - How many ways can three cars be parked in a row of four ...

math - how many ways can 9 cars be parked in a row of 9 parking spaces?

Math - How many ways can 9 cars be parked in a row of 9 parking spaces? Answer: ...

Math - I need help step by step on how to figure how many ways can three cars be...

math***check answerss**** - please check answers... 2.yesterday ,a parking lot ...

math - There are 25 cars in a parking lot. Nine of the cars are red. The rest ...

math - Assume that you are to pick 3 cars from the motor pool, which contains 6 ...