AMC 12A 2021 Spring Problem 15

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 groups that can be selected. What is the remainder when N is divided by 100 ?

Answer Choices
A. 47
B. 48
C. 83
D. 95
E. 96