Prephub - 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 basses must be a multiple of 4 and the group must have 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

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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 basses must be a multiple of $4$ , and the group must have 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 $100 ?$

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