Discrete Mathematics Level 4

Ron wants to create a song that consists of the following phrases:

  • "Aashyman Aashyman"
  • "Jacku Jacku"
  • "Carly Carly"
  • "Csajah Csajah"
  • "Curry Curry"
  • "Chikun Chikun"
  • "Chhhhhikuuuuuuuuuun"
  • "Nowy Nowy"
  • "Ronnam Ronnam Nowy Nowy Ronnam Wisda Taichi!"
  • "Eh Eh"

He wants the song to have 4 verses, and each verse to have 3 phrases. Each phrase has to appear at least once.

Moreover, he wants the phrases "Ronnam Ronnam Nowy Nowy Ronnam Wisda Taichi!", "Eh Eh"and "Chhhhhikuuuuuuuuuun" to always be the last phrase of a verse.

Let the Number of songs Ron can make be \(a\), find the remainder when the product of the non-zero digits of \(a\) is divided by 1000.

Note: this question was inspired by this awesome song


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