Engineering
Mathematics
Permutation and Combination Basic Definitions
Question
Let X = {1, 2, 3, 4, 5}. The number of different ordered pairs (Y, Z) that can be formed such that Y ⊆ X, Z ⊆ X, and Y ⋂ Z is empty, is :
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Solution
1 can be distributed in two set Y and Z by 3 ways.
2 can be distributed in two set Y and Z by 3 ways.
3 can be distributed in two set Y and Z by 3 ways.
4 can be distributed in two set Y and Z by 3 ways.
5 can be distributed in two set Y and Z by 3 ways.
(The three ways are either only in Y or only in Z or in none of Y and Z.)
∴ Number of way of distributing each element = 35.
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