Satu paket siomay terdiri dari $10$ buah, yakni dapat terdiri dari siomay, tahu, telur, kentang, kol, dan pare. Jika tidak suka pare atau kol, bisa diganti dengan bahan lain. Jumlah pare dan kol maksimal $1$ buah. Telur harus $1$ buah dan siomay minimal $3$ buah. Banyak cara pemilihan isi satu paket Siomay adalah... $\newline$ A $80$ cara $\newline$ B $82$ cara $\newline$ C $85$ cara $\newline$ D $88$ cara $\newline$ E $92$ cara

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Q. Satu paket siomay terdiri dari

10

buah, yakni dapat terdiri dari siomay, tahu, telur, kentang, kol, dan pare. Jika tidak suka pare atau kol, bisa diganti dengan bahan lain. Jumlah pare dan kol maksimal

1

buah. Telur harus

1

buah dan siomay minimal

3

buah. Banyak cara pemilihan isi satu paket Siomay adalah...

\newline

80

cara

\newline

82

cara

\newline

85

cara

\newline

88

cara

\newline

92

cara

Identify total number of items: Identify the total number of items in one package, which is $10$ .
Choose mandatory egg: Since $1$ egg is mandatory, we now have $9$ items left to choose.
Add siomay to package: Since siomay is at least $3$ pieces, let's add those to the package. Now we have $6$ items left.
Consider pare or kol: We can have at most $1$ piece of pare or kol. Let's consider the scenarios where we have $0$ or $1$ of these.
Calculate combinations with $0$ pare/kol: If we choose $0$ pare/kol, we have $6$ items left to fill with siomay, tahu, telur, kentang. Since we already have $1$ egg, we can't choose more eggs. So we have $3$ options for each of the $6$ items.
Calculate combinations with $1$ pare/kol: Calculate the number of combinations with $0$ pare/kol: $3^6 = 729$ ways.
Add combinations from both scenarios: If we choose $1$ pare/kol, we have $5$ items left to fill with siomay, tahu, telur, kentang. Again, no more eggs, so $3$ options for each of the $5$ items.
Add combinations from both scenarios: If we choose $1$ pare/kol, we have $5$ items left to fill with siomay, tahu, telur, kentang. Again, no more eggs, so $3$ options for each of the $5$ items.Calculate the number of combinations with $1$ pare/kol: $2$ (for choosing pare or kol) $\times 3^5 = 2 \times 243 = 486$ ways.
Add combinations from both scenarios: If we choose $1$ pare/kol, we have $5$ items left to fill with siomay, tahu, telur, kentang. Again, no more eggs, so $3$ options for each of the $5$ items.Calculate the number of combinations with $1$ pare/kol: $2$ (for choosing pare or kol) $\times 3^5 = 2 \times 243 = 486$ ways.Add the combinations from both scenarios: $729$ (with $0$ pare/kol) + $486$ (with $1$ pare/kol) = $5$ $1$ ways.