The number of different 5 digit numbers greater than 50000 that can be formed using the digits 0 , $1,2,3,4…

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
  1. 4608
  2. 5720
  3. 5719
  4. 4607

Solution

$\begin{array}{lll}
\text { Case I } & 5 \ldots \ldots & 0 \\ \text { Case II } & 5 \ldots \ldots & \\ & 5 & 1 \\ & 5 & 3 \\ & 6 & 0 \\ & 6 & 1 \\ & 6 & 2 \\ & 7 & 0 \\ & 7 & 1
\end{array}$
$9 \times(8 \times 8 \times 8)=4608$ but 50000 is not included, so total numbers $4608-1=4607$ .

Asked in: JEE Main 2025 (28 Jan Shift 1)

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