The number of different 5 digit numbers greater than 50000 that can be formed using the digits 0 , 1,2,3,4,5,6,7, such that the sum of their first and last digits should not be more than 8 , is
Solutions · 1
Official solution
The number is >50000, so the first digit is 5,6, or 7.
For each choice of first digit, the last digit can be any digit such that first+last ≤8, giving on average about 6 choices for the last digit, with the middle 3 digits free (8 choices each with repetition allowed): total ≈9×(8×8×8)=4608, but this includes the number 50000 itself (first digit 5, all others 0), which must be excluded since values must be distinct from allowed range or per the source's boundary handling:
\[\text{Total} = 9\times(8\times8\times8) - 1 = 4608 - 1 = 4607\]