Answer:
4-digit numbers with distinct digits and greater than 4500: 2800 numbers
5-digit numbers with distinct digits: 27216 numbers.
Step-by-step explanation:
If we represent a 4 number digit by ABCD, we have 9 posibilities for A (1,2,3,4,5,6,7,8 and 9, all but 0).
If every digit has to be different, we have 9 posibilities for B: ten digits (0,1,2,3,4,5,6,7,8 and 9 minus the one already used in A).
Int he same way, we have 8 posibilities for C and 7 for D.
Considering all 4-digits numbers, we have 9*9*8*7 = 4536 numers with distinct digits.
To know how many of these numbers are greater than 4500, we can substracte first the numbers that are smaller than 4000: A can take 3 digits (1,2 and 3) and B, C and D the same as before.
3*9*8*7 = 1512 numbers smaller than 4000
Then we can substrat the ones that are between 4000 and 4500
1*4*8*7 = 224 numbers between 4000 and 4500
So, if we substract from the total the numbers that are smaller than 4500 we have the results:
4-digit numbers with distinct digits greater than 4500 = 4536-(1512+224) = 2800
For 5-digit numbers, we can call the number ABCDE.
For A we have 9 digits possible (all but 0).
For B, we also have 9 posibilities (all digits but the one used in A).
For C, we have 8 digits (all 10 but the ones used in A and B).
For D, we have 7 digits.
For E, we have 6 digits.
Multiplying the possible combinations, we have:
9*9*8*7*6 = 27,216 5-digit numbers with distinct digits.
