Enclave radio problem

Discrete Mathematics Level 4

It is a perfect, cloudless day... the Sun is warm and welcoming... and today is the day, dear everyone, when John Henry Eden is going to organize the radio's afternoon schedule. All by himself. That's right, no one will help him, he will do it all alone. In today's afternoon schedule, he is planning to play 7 music pieces and 4 brand new speeches. Music and speeches are, of course, unique. And JHE has decided the following:

  • The afternoon program will begin with a speech.

  • The afternoon program will end with a music piece.

  • Between any two speeches, there must be a pause, filled with at least one music piece.

All of a sudden, JHE has started thinking about math, or to be more precise, about discrete math. He is thinking, on how many different ways, he can accomplish organization of today's afternoon program.

And now, dear Brilliant Solvers, it is Your time to shine, help JHE in his math trouble, and let him make today's afternoon program great, once again.


Available music pieces shall be labelled as { 1, 2, 3, 4, 5, 6, 7 }, whilst available speeches will be labelled as { A, B, C, D }. Here are three (different) example of satisfying ways to organize schedule:

  • A12B34C56D7

  • A12B34C65D7

  • A1234B5C6D7

If there is any questions, they can be asked here.


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