Question

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

Answer 1

Answer:

Total number = 3000

Step-by-step explanation:

Odd digit numbers = 1,3,5,7,9

Total no. of odd digit numbers = 5

Numbers which aren't odd = 0,2,4,6,8

Total no. which aren't odd = 5

For a 4 digit number.

If all Fours digits are odd:

Total numbers = 5×5×5×5 = 625

If first digit is not odd and last three digits are odd:

Total numbers = 4×5×5×5 = 500

(0 cannot be put at first digits place)

If second digit is not odd and rest three digits are odd:

Total numbers = 5×5×5×5 = 625

If third digit is not odd and rest three digits are odd:

Total numbers = 5×5×5×5 = 625

If fourth digit is not odd and rest three digits are odd:

Total numbers = 5×5×5×5 = 625

Add all of them we get:

Total number = 625+500+625+625+625 = 3000