Help on Permuntation and Combination Question

[fluffy91]

[SOLVED] Help on Permuntation and Combination Question

Homework Statement

After a show ,they decided to divide into two groups of size four and five, to go for a supper in 2 taxis. In how many ways could this be done if george and sally were to be in the same taxi

Homework Equations

nCn
nPc

The Attempt at a Solution

No of ways = (3p3 x 2! + 4p4)+(2p2 x 2! + 5p5) = 160

But answer is 56. How do u get the answer it is so small

 

[Sleek]

Taxi A and B have capacities 4,5 resp.

They both (George, Sally) can be either in Taxi A or B. If they're in taxi A, how many more people do you have to select from 7 remaining and in how many ways? And in the second case (taxi B), how many more do you need from 7? Add them up to get your answer.

You need to find the number of ways of selecting 2 and 3 people from 7. Can you see why? Also, the order in which you select the 2 or 3 doesn't matter. Also, the remaining people would occupy the second taxi. So you only need to consider the taxi in which Sally, George are sitting.

The answer indeed is 56.

Regards,
Sleek.

 

[fluffy91]

OK Thanks so it was C instead of P. Question solved

 

[Gib Z]

OK Thanks so it was C instead of P. Question solved

That doesn't sound like you really understand the situation, rather that you learn to insert things into equations :( To distinguish between a Permutation and a Combination, consider if order matters. For the taxis, it doesn't because if ABC get into 1 taxi, its the same as BAC etc etc.