Question

To use an automated teller machine at a certain​ bank, you must enter a 6​-digit ​code, using the digits 0–9. How many 6​-digit codes are possible if repetition of digits is​ permitted?

Answer 1

answer is 1,000,000

there are total 10 digits (0,1,2,3,4,5,6,7,8,9)

first digit of 6​-digit codes may be filled by any of given 10 digits with number of way=10

2nd digit of 6​-digit codes may be filled by any of given 10 digits with number of way=10

3rd digit of 6​-digit codes may be filled by any of given 10 digits with number of way=10

4th digit of 6​-digit codes may be filled by any of given 10 digits with number of way=10

5th digit of 6​-digit codes may be filled by any of given 10 digits with number of way=10

6th digit of 6​-digit codes may be filled by any of given 10 digits with number of way=10

so required number of way=10*10*10*10*10*10=1,000,000

answer is 1,000,000