Question

How many six-digit numbers have all their digits of equal parity (all odd or all even)? PLS EXPLAIN

Answer 1

Answer:

28,125

Step-by-step explanation:

There are 10 digits between 0 and 9.  5 of them are odd, and 5 of them are even.

If a six-digit number has all odd digits, then there are 5 numbers that can be the first digit, 5 numbers that can be the second digit, 5 numbers that can be the third digit, and so on.

The number of permutations is 5×5×5×5×5×5 = 5⁶ = 15,625.

For all even digit numbers, the first digit can't be 0, so the number of permutations is 4×5×5×5×5×5 = 4×5⁵ = 12,500.

So the total permutations of six-digit numbers of equal parity is 15,625 + 12,500 = 28,125.