GeneratingFunction Difficult

Problem - 2536

How many different $5$-digit numbers can be formed using $1$, $2$, $3$, and $4$ that satisfy the following conditions:

  • the digit $1$ must appear either $2$ or $3$ times,
  • the digit $2$ must appear even times,
  • the digit $3$ must appear odd times, and
  • the digit $4$ has no restriction

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