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1 answer:
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Answer:
Proved
Step-by-step explanation:
From the given parameters, we have:
i.e. the length of each security numbers
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:
Apply Pigeonhole principle
The principle states that: suppose there are n items in m containers, where , 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.
Answer: They meet after 1 hour 42 minutes.
Step-by-step explanation:
Since we have given that
Dana leaves Las Vegas for LA at 2 p.m. driving at 55 mph.
Let the time taken by Dana be 't'.
Distance traveled by Dana would be 55t.
At 4 p.m. Lance leaves LA for Las Vegas driving at 45 mph along the same route.
It means after 2 hours Lance leave for LA.
So, time taken by Lance be 't-2'.
Distance traveled by Lance would be 45(t-2)
Total distance = 260 miles
According to question, it becomes,
Hence, they meet after 1 hour 42 minutes.