JEE MAIN - Mathematics (2025 - 28th January Morning Shift - No. 16)
The number of different 5 digit numbers greater than 50000 that can be formed using the digits 0 , $1,2,3,4,5,6,7$, such that the sum of their first and last digits should not be more than 8 , is
5720
5719
4608
4607
Explanation
Case I $5{ }_{---} 0$
Case II $5{ }_{---} 1$
$$ \begin{array}{ll} 5 & 2 \\ 5 & 3 \\ 6 & 0 \\ 6 & 1 \\ 6 & 2 \\ 7 & 0 \end{array}$$
Case IX $7{ }_{---} 1$
$9 \times(8 \times 8 \times 8)=4608$ but 50000 is not included, so total numbers $4608-1=4607$
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