The correct answer or possible sequence is the value of N/10 is 372.
The letters can be selected from the words "AIME" or "2007."
The only number that can be repeated twice is 0; there are seven different characters that can be chosen.
There are two potential scenarios.
Here is the first instance:
There are 7!/(7-5) potential sequences if 0 appears 0 or 1 times in the sequence.
There are 2520 possible sequences if 0 appears 0 or 1 times in the sequence.
Here is the second example:
If 0 occurs twice in the sequence, there must be a 0 in ⁵C₂. positions.
If 0 occurs twice in the sequence, 10 spots must be filled with 0.
The remaining three characters can be arranged in 6!/(6-3)! different ways.
There are 120 different arrangements for the final three characters.
In the second scenario, there are a total of 1200 possible possibilities, or 10*120.
There are 2520 methods in total plus 1200.
There are 3720 different ways in all.
N = 3720
We must ascertain the value of (N/10)
⇒ N/10 = 3720/10
⇒ N/10 = 372
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