series of questions on permutations and combinations (1 Viewer)

[martin310015]

need help on the following questions

1. mr and mrs jones and 6 guests sit around the dinner table. in how many ways can they be arranged if the two hosts are separated?

2. in how many ways can a committee of 3 women and 4 men be chosen from 8 women and 7 men if two particular women refuse to serve on the committee together?

3. eight points are equally spaced on the circumference of a circle.
chords may be joining any two points. how many chords can be drawn which are not diameters?

THANX

 

[-=«MÄLÅÇhïtÊ»=-]

The easiest way to do these is to use complementary cases.

1) If there are no conditions, there would be 7! ways
If the hosts sit together there would be 6!*2 ways
So required answer is 7! - 6!*2 = 3600


2) With no conditions, there would be 8C3*7C4 ways
If the 2 women who despise each other serve together there would be 6C1*7C4 ways
So required answer is 8C3*7C4 - 6C1*7C4 = 1750


3) Joining 8 dots around the circle is really the same thing as arranging the 8 dots around the circle. So with no conditions, there are 7! ways of doing that. There are 8/2 possbile diameters. So the required answer is 7! - 4 = 5036

 

[flyin']

That's ACST211 in action!

 

[martin310015]

thank u very much

 

[Grey Council]

lol, two actuary students! kill those hsc permutation questions, come on. lol