Question

Six-digit odd numbers, greater than $6,00,000$ that can be formed using the digits $5,6,7,8,9$ and $0$ if repetition of digits is not allowed is :

• A. $4\times 6^5$
• B. $240$
• C. $560$
• D. $60$

Answer 1

The correct option is B $240$

We have $6$ digits, $5,6,7,8,9$ and $0$ and we have to form odd numbers greater than $6,00,000$

The unit's place can only be filled by $5,7$ or $9$ since we have to form odd numbers.

The first place (lakh's position) can be occupied by the digits greater than or equal to $6$.

Since, repetition is not allowed, therefore -

$\begin{array}{ccc}& \text{Digits in lakh's place}& \text{Digits in the unit's place}\\ \text{(I)}& 6& 5,7,9\\ & & \\ \text{(II)}& 7& 5,9\\ & & \\ \text{(III)}& 8& 5,7,9\\ & & \\ \text{(IV)}& 9& 5,7\\ & & \end{array}$

Thus the required six digit numbers possible are
$\text{(I)}4!+4!+4!$
$\text{(II)}4!+4!$
$\text{(III)}4!+4!+4!$
$\text{(IV)}4!+4!$
$=10\times 4!=240$