Question

How many positive integers between 1000 and 3999, inclusive
1. have no repeated digit?
2. have at least one repeated digit?
3. have at most two repeated digit?

note. example 1123 has one repeated digit. two repeated digits = 1112

Answer 1

Answer:

1512  numbers have no repeated digit

1488 Number having atleast one repeated digit

Step-by-step explanation:

How many positive integers between 1000 and 3999, inclusive

1. have no repeated digit?

note. example 1123 has one repeated digit. two repeated digits = 1112

positive integers between 1000 and 3999, inclusive

1. have no repeated digit

1st digit would be 1 to 3    - 3 digits

Second digit would be from 0 to 9 excluding 1st digit -   9 digits

Third digit would be from 0 to 9 excluding 1st two digit - 8 digits

Fourth Digits would be from 0 to 9 excluding 1st three digit - 7 digits

Total numbers = 3 * 9  * 8 * 7 = 1512

1512  numbers have no repeated digit

2. have at least one repeated digit

1000 - 3999  total numbers = 3000

Number having no repeated digits = 1512

Number having atleast one repeated digit = total numbers - numbers with no repeated digits

= 3000 - 1512

= 1488

Number having atleast one repeated digit = 1488