Question

How many even numbers of three digits can be formed with the digits $0,1,2,3,4,5$ and $6?$

• A. $121$
• B. $168$
• C. $105$
• D. $125$

Answer 1

The correct option is C $105$

Three digit number $⟶$ even

No repetition

$0,1,2,3,4,5,6$

last digit should be $0,2,4,6$

Case : $1$ Zero at last

and other two places six digits can be placed

${\Rightarrow }^6{P}_2=30$

Case :$2$ when $2,4,6$ at last

means last digit can have three possiblity

other two places have five five possiblity each

$\Rightarrow 5\times 5\times 3=75$

Total possiblity

$\Rightarrow 30+75\Rightarrow 105ways$