Question

Find the number of six digit odd numbers that are greater than $60000$ and can be formed with the digits $5,6,7,8,9,0$ when repetition is not allowed.

• A. $150$
• B. $120$
• C. $480$
• D. $240$

Answer 1

The correct option is D $240$

$5,6,7,8,9,0$

Numbers greater than $60000$

Case: 1 First position is $6$ Other $4$ places by $(5,7,9)$

$3\times 4\times 3\times 2=72$

Case: 2 First position is $7$ Other $4$ places by $(5,9)$

$2\times 4\times 3\times 2=48$

Case: 3 First position is $8$ Other $4$ places by $(5,7,9)$

$3\times 4\times 3\times 2=72$

Case: 4 First position is $9$ Other $4$ places by $(5,7,9)$

$2\times 4\times 3\times 2=48$

Total possible numbers $=72+48+72+48=240$