Q44 / 75 · JEE Main 2025 (28 Jan Shift 1) · Mathematics

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

A
4608
B
5720
C
5719
Correct answer
D
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 $4608-1=4607$

Hence, the correct answer is option: 'D'.

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