# Perms and Combs problem

by physics kiddy
Tags: combs, perms
 P: 135 Here's the problem : Let X = {1,2,3,4 ...... 10}. Find the number of pairs {A,B} such that A $\subseteq$ X and B $\subseteq$ X, A $\neq$ B and A $\cap$ 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 ....
 Homework Sci Advisor HW Helper Thanks ∞ P: 9,205 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.

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