# Thread: [SOLVED] Counting Problem - just a quick question with this problem

1. ## [SOLVED] Counting Problem - just a quick question with this problem

Q: How many positive integers between 1000 and 9999 inclusive are divisible by 9?
A: 9999 - 1000 + 1 = 9000

This question is part c.
Q: How many positive integers between 1000 and 9999 inclusive are distinct digit?
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part c I do not understand.
I have the answer as 9 x 9 x 8 x 7 = 4536. But I do not get why the 0 is not included in the 1st digit but the 0 is included in the 2nd?

This is what was given by my instructor:
1st digit is 9
2nd digit is 10 - 1 = 9
3rd is 10 - 2 = 8
4th is 10 -3 = 7
This is where he got 9 x 9 x 8 x 7.

2. Why ?
What is the wrong with your instructors answer ?
1st digit - 1,2,3,4,5,6,7,8,9 (9digits)
2nd digit - since we have selected 9 natural digits for the digit we have 8 more such digits but we can use zero for 2 nd digit . (therefore 9 digits again)
3rd digit - we have 8 digits
4th digit - we have 7 digits

As you said if we have 0 for the 1st digit it will be less than 1000 ?
wont it be ?

3. forget about it....I just figured it out.

4. Originally Posted by K A D C Dilshan
Why ?
What is the wrong with your instructors answer ?
1st digit - 1,2,3,4,5,6,7,8,9 (9digits)
2nd digit - since we have selected 9 natural digits for the digit we have 8 more such digits but we can use zero for 2 nd digit . (therefore 9 digits again)
3rd digit - we have 8 digits
4th digit - we have 7 digits

As you said if we have 0 for the 1st digit it will be less than 1000 ?
wont it be ?
Think what happens if you select 0 for the 1st digit ...
It will make your number less than 1000 .
Can you understand it ?

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# how many positive integers between 1000 and 9999 inclusive are divisible by 5 and 7

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