Register to reply

Perms and Combs problem

by physics kiddy
Tags: combs, perms
Share this thread:
physics kiddy
#1
Jan2-13, 11:18 AM
P: 135
Here's the problem :

Let X = {1,2,3,4 ...... 10}. Find the number of pairs {A,B} such that A [itex]\subseteq[/itex] X and B [itex]\subseteq[/itex] X, A [itex]\neq[/itex]
B and A [itex]\cap[/itex] B = {5,7,8}.

My attempt:

Once we know that the remaining numbers are 1,2,3,4,6,9,10 ... a total of 7 numbers, we can use permutation to know that seven elements can be distributed to 2 sets in 2^7 ways ...

Excluding A and B having the common elements {5,7,8}, we have a total of 2^7-1 such numbers A and B.

However the answer is 3^7 - 1. I don't know how ....
Phys.Org News Partner Science news on Phys.org
Bees able to spot which flowers offer best rewards before landing
Classic Lewis Carroll character inspires new ecological model
When cooperation counts: Researchers find sperm benefit from grouping together in mice
haruspex
#2
Jan2-13, 03:18 PM
Homework
Sci Advisor
HW Helper
Thanks
P: 9,656
There would be 27 ways of placing each of the 7 remaining digits in either A or B. But they need not be in either.


Register to reply

Related Discussions
Math 20: Perms & Combs Help. Precalculus Mathematics Homework 1
Question from Perms and Combs unit Precalculus Mathematics Homework 5
Perms and Combs Introductory Physics Homework 2
Perms/combination questions General Math 2
Chicken combs Biology 4