Question

How many numbers greater than 200 and divisible by 2 can be made from the digits 4, 5, 6, and 7 if no digit is repeated. 

Options

• 6

• 12

• 24

• 30

Answer 1

12

Explanation: 

Numbers that are divisible by 2 must have '4' fixed in the extreme right place

3 Digit Numbers			4 Digit Numbers
H	T	U	Th	H	T	U
×	×	4	×	×	×	4
`""^3"P"_2` ways = `(3!)/(1!) = 3 xx 2 = 6`			`""^3"P"_3` ways = `(3!)/(0!) = 3 xx 2 = 6`

⇒ Total ways = 6 + 6 = 12