Question

How many number greater than 1000000 can beformed by using digits 1,2,0,2,4,2,4?

Answer 1

let the number be x.

x10,00,000.

digits we are allowed to use are 1,0,2,2,4,2,4.

there are 7 numbers and we can arrange them in 7! ways:

7*6*5*4*3*2*1.

since we are not allowed to repeat the numbers and 4 is repeated twice and 2 is repeated thrice,we he to divide it by 3! and 2!v(4arranged in 2! ways and 2 arranged in 3! ways)

=7*6*5*4*3*2*1/3*2*1*2*1

=210*2

=420.

but since this number has to greater than 10,00,000;

the first number cannot be 0.

now we are left with 6 numbers we can choose from and these can be arranged in 6! ways:

6*5*4*3*2*1.

since repetion not allowed: 2!*3!(same reason).

=6*5*4*3*2*1/3*2*1*2*1;

=60.

therefore,the no.of numbers greater then 10,00,000 is

=(7!/2!*3!)-6!/2!*3!)

=420-60

=360.

Therefore there are 360 numbers greater then 10,00,000.

hope it helps :) cheers!