What is the number of arrangements of 10 different things taken 4 at a time in which one particular thing always occur?

Suppose I want to pick 4 of the digits 0-9, but I want to always include 9. Then, I have 9xyz or x9yz or xy9z or xyz9. That is, I have four different arrangements for any particular choice of x, y, and z. Assuming I don't allow xyz to contain 9, I need to find the number of arrangements of 9 things taken 3 at a time. That number is (9)(8)(7) = 504.

If there are four (4) possible arrangements that include 9 for each of the 504 choices of xyz, then the total number of arrangements is 4(504) = 2016.

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If one of the numbers never occurs, I'm looking at counting the arrangements of 9 things taken 4 at a time. That is (9)(8)(7)(6) = 6(504) = 3024.

How many of the permutations of 10 different things taken 4 at a time with one particular thing : a Never occur b Always occur.

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