A choir director must select a group of singers from among his 6 tenors and 8 basses. The only requirements are that the difference between the number of tenors and the number of basses must be a multiple of four, and that the group must contain at least one singer. Let N be the number of different groups that could be selected. What is the remainder when N is divided by 100?

Source: AMC 12A 2021

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