Question

If you have the digits 0-6 and there is no restrictions on repetitions and/or zeros, calculate how many possible 4 digit arrangements you can have that contain at least one even digit. Show work

Answer 1

Distinct Numbers with Repetition, All Numbers are used: If an n distinct number string has to be arranged, with repetition using all the numbers say x, then the total number of ways of arranging the same is n^x.

The digits are 0, 1, 2 , 3, 4, 5 and 6...7 digits of which 2, 4 and 6 (3 digits) are even and the rest 0, 1, 3 and 5 (4 digits) are not even.

The total number of arrangements = 7 * 7 * 7 * 7 = 2401

Number of arrangements where there is not a single even number = 4 * 4 * 4 * 4 = 256

Therefore number of arrangements which have at least 1 even number = 2401 - 256 = 2145