PDA

View Full Version : 2 Combination/Permutation problems for ya....



Rishad
12-25-2002, 03:29 AM
Hi guys, does anyone have a way to do these? thanks.....

1. Out of 7 models, all of different sizes, 5 models will be chosen to pose for a photograph. If the 5 models are to stand in a line from shortest to tallest, and the 4th-tallest and 6th-tallest models can't be adjacent, how many different arrangements are possible?
6
11
17--- this is correct but don't know why
72
210

2. If you have 5 square picture frames, all of varying sizes, and you want to hang them on a wall in a row, how many combinations exist such that the two largest frames are never next to each other?

frt222
01-18-2003, 02:06 PM
Here is one way to solve this. Without the constraint of the the 4th and 6th models not standing together, the number of ways to arrange the models is 7C5 which gives us 21. Now eliminate the impossible combinations

12346 23467 13467 12467

which gives the correct answer of 21 -4 = 17.

Ravi

avc
01-25-2003, 12:00 AM
hello Rishad,
what is the correct answer for the second problem ?
Is it 96 ?

-avc

dmonica
01-29-2003, 05:37 PM
Hi Rishad,

Is it the answer 72? I think that the general formula is
(n-2)(n-1)!

dmonica