Combinatorics BasicSequence Exeter Intermediate

Problem - 2043
Chad has $100$ cookies that he wants to distribute among four friends. Two of them, Jeff and Qiao, are rivals; neither wants the other to receive more cookies than they do. The other two, Jim and Townley, don't care about how many cookies they receive. In how many ways can Chad distribute all $100$ cookies to his four friends so that everyone is satisfied? (Some of his four friends may receive zero cookies.)

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