A video$-$streaming Web site keeps count of the number of times each video has been played since it was first added to the site. The count is updated each time a video is played and is displayed next to each video to show its popularity.

At one time, the count for the most popular video was about two million. Sometime later, the same video displayed a seven$-$digit negative number as its count, while the counts for the other videos displayed correctly. Which of the following is the most likely explanation for the error?

a$.$ The count for the video became larger than the maximum value allowed by the data type used to store the count

b$.$ The mathematical operations used to calculate the count caused a rounding error to occur.

c$.$ The software used to update the count failed when too many videos were played simultaneously by too many users.

d$.$ The software used to update the count contained a sampling error when using digital data to approximate the analog count.