1, 2, 3, 4, and 5, when (a) repetition is not allowed and (b) repetition is allowed. Briefly explain the calculation process.
We can form numbers starting with 3, 4, or 5.
a)
If a number start with digit "3", then we can choose 2nd and 3rd digit by choosing two digits from "\\{1,2,4,5\\}"
Without repetition, this is:
"C^2_4=\\frac{4!}{2!2!}=6" ways
The same is for numbers starting with digit "4" or "5".
So, total number of ways:
"N=6+6+6=18"
b)
If a number start with digit "3", then we can choose 2nd and 3rd digit by
"5\\cdot5=25" ways
The same is for numbers starting with digit "4" or "5".
So, total number of ways:
"N=25+25+25=75"
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