Question

Find the number of 4-digit numbers that contain at least three odd digits.

Answer 1

3000

Explanation:

4*5*5*5+5*5*5*5+5*5*5*5+5*5*5*5+5*5*5*5 = 3000

Answer 2

3000

Explanation:

First find the 4 digit numbers that have all odd digits

Possible Odd digits =5(1,3,5,7,9)

So, total number of 4 digit numbers with odd digits can be calculated as =5×5×5×5=625

Now find all the 4 digits numbers with at least 3 odd digits and the first digit as either 2,4,6,8 ( 0 would make it a 3 digit number)

The first digit can be 2,4,6,8

=4×5×5×5=500

Now find all the 4 digits numbers with at least 3 odd digits and the second digit as either 0,2,4,6,8

=5×5×5×5=625

Now find all the 4 digits numbers with at least 3 odd digits and the third digit as either 0,2,4,6,8

Now find all the 4 digits numbers with at least 3 odd digits and the second digit as either 0,2,4,6,8

=5×5×5×5=625

Now find all the 4 digits numbers with at least 3 odd digits and the fourth digit as either 0,2,4,6,8

=5×5×5×5=625

Add them together

625+500+625+625+625=3000