Question

How many 5 digit numbers exist, whose first and last digit are the same

Answer 1

You have 9 options for the first digit (1, 2, 3,…, 9) - 9 ways.

For the second digit you can use each digit except for the one you used for the first one, so these are 10 - 1 = 9 ways.

For the third digit you can choose any digit except for the first two (10 - 2 = 8 ways).

For the fourth digit we have 10 - 3 = 7 ways and for the fifth one - 10 - 4 = 6 ways.

Now we just multiply them to get the total count of possible 5=digit numbers - 9*9*8*7*6=27216 numbers.

Answer 2

first digit = 9

last digit = 9

MAXIMUM SUM CAN BE 5 × 9 = 45

Now , see that 5k,3k+1,5k+3 can't be a tuple of solution.