How many 5-digit numbers have an even sum of digits?

But, we are interested in the numbers whose sum is even so it will be half of the total five digit numbers, so the answer is 1 2 × ( 9 × 10 × 10 × 10 × 10) which is 45000. There are 90000 5 -digit numbers, exactly half have an even sum of digits (base 10 has equal numbers of even and odd digits)

How many ways can you choose the first digit of a number?

The first digit can be chosen in 9 ways (since it can’t be a 0), the second in 10 ways, the third in 10 ways, the fourth in 10 ways, and the fifth in five ways (the last digit must be one of the five even digits if the first four digits add up to an even number, and odd otherwise, so that the total sum is even).

Why do s and E partition the collection of 5 digit numbers?

S and E partition the collection of all 5 digit numbers and S does not contain 99999. Adding 1 to elements of S gives elements of E. This function is from S to E and is in fact a bijection and so both sets contain equal number of elements.

How many six-digit positive integers have three digits that each appear twice?

Therefore, the number of six-digit positive integers in which there are three digits that each appear twice is You counted each such case twice. For instance, take the number 837783. You counted it in two ways: You selected 8 as the leading digit, then chose to place it in the fifth position.

What is the total number of choices for the first digit?

For the third number, there are 4 choices, for the fourth number there are 3 choices, and for the fifth number there are 2 choices. Thus, the total number of choices is (5) (5) (4) (3) (2) = 600. Alternatively, use the same logic and realize there are 5 choices for the first digit.

What is the total number of combinations possible with 5 numbers?

Overall, every one of the 5 places of a 5-digit number can be filled up in ten ways, because it can have 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9. So each of the five places can be similarly filled up in ten ways. Therefore, the total number of combinations possible are 10 × 10 × 10 × 10 × 10 = 1,00,000.

How many ways can a 5-digit number be filled up?

A five-digit number cannot have 0 as the first digit on the left, which is the ten thousand place. Overall, every one of the 5 places of a 5-digit number can be filled up in ten ways, because it can have 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9. So each of the five places can be similarly filled up in ten ways.