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Sagot :
Answer:
Proved
Step-by-step explanation:
From the given parameters, we have:
[tex]n = 9[/tex] i.e. the length of each security numbers
[tex]r = 2[/tex] i.e. 2 security numbers
Required
In 513 security numbers, 2 must have matching zeros
To do this, we make use of Pigeonhole principle.
First, we calculate the number of all security numbers not having matching zeros.
Each of the 9 digits can be selected in 2 ways.
2 ways implies that each digit is either 0 or not
So, total selection is:
[tex]Total = 2^9[/tex]
[tex]Total = 512[/tex]
Apply Pigeonhole principle
The principle states that: suppose there are n items in m containers, where [tex]n>m[/tex], then there is at least one container that contains more than 1 item.
This means that if there are 512 security number without matching zeros, then there is 1 (i.e. 512 + 1) with matching zeros.
[tex]512 + 1 = 513[/tex]
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