How many numbers greater than 1000000 can be formed by using the digit

1.	How many numbers greater than 1000000 can be formed by using the digits 1, 2,0,2,4,2,4?
Answer» Since the required numbers are greater than 1000000, then the number is begin with either 1,2 or 4 ∴ Number of numbers begin with 1 = 6!/3!2! = (6 x 5 x 4 x 3!)/3!(2 x 1) = 60 Total numbers beginning with 2 = 6!/2!2! = (3 x 4 x 5 x 6)/2 = 180 Total numbers beginning with 4 = 6!/3! = 6 x 5 x 4 = 120 Required number of numbers = 60+ 180 + 120 = 360 Alternative Required number of numbers = 7!/3!2! - 6!/3!2! = 420 - 60 = 360

How many numbers greater than 1000000 can be formed by using the digits 1, 2,0,2,4,2,4?

Answer»

Since the required numbers are greater than 1000000, then the number is begin with either 1,2 or 4

∴ Number of numbers begin with 1

= 6!/3!2! = (6 x 5 x 4 x 3!)/3!(2 x 1) = 60

Total numbers beginning with 2

= 6!/2!2! = (3 x 4 x 5 x 6)/2 = 180

Total numbers beginning with 4

= 6!/3! = 6 x 5 x 4 = 120

Required number of numbers

= 60+ 180 + 120 = 360

Alternative

Required number of numbers

= 7!/3!2! - 6!/3!2! = 420 - 60 = 360