Question

How many $6$ digits odd numbers greater than $60,0000$ can be formed from the digits $5,6,7,8,9,0$ if
(i) repetitions are not allowed (ii) repetitions are allowed

Answer 1

(a)$\Rightarrow {(}^4{C}_1).\lfloor 5\to$ arrangement of remaining $5$ after selection $1$

$\downarrow$

Selection from $6,7,8,9$

$=4\times \lfloor 5$

(b) $\Rightarrow \left(4\right).\left(6\right)\left(6\right)\left(6\right)\left(6\right)\left(6\right)$

$\downarrow$

only four choices $\Rightarrow (6,7,8,9)$

$=31104$ Answer