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Untuk meperoleh jenis baru, dilakukan penyilangan terhadap 10 jenis padi yang berlainan satu sama lain. Banyak cara yang mungkin sebanyak......cara

Untuk meperoleh jenis baru, dilakukan penyilangan terhadap $10$ jenis padi yang berlainan satu sama lain. Banyak cara yang mungkin sebanyak......cara

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Find the sum of an arithmetic series

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Q. Untuk meperoleh jenis baru, dilakukan penyilangan terhadap

10

jenis padi yang berlainan satu sama lain. Banyak cara yang mungkin sebanyak......cara

Understand Combination Problem: To determine the number of different ways $10$ distinct rice varieties can be crossed with each other, we need to understand that each variety can be crossed with every other variety. This is a combination problem where order does not matter, and we are choosing $2$ out of $10$ . The formula for combinations is $C(n, k) = \frac{n!}{k!(n-k)!}$ , where $n$ is the total number of items, and $k$ is the number of items to choose. Here, $n = 10$ and $k = 2$ .
Calculate Factorial of n: First, we calculate the factorial of $n$ , which is $10!$ ( $10$ factorial). $10! = 10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1$ .
Calculate Factorial of $k$ : Next, we calculate the factorial of $k$ , which is $2!$ ( $2$ factorial). $2! = 2 \times 1$ .
Calculate Factorial of $(n-k)$ : We also need to calculate the factorial of $(n-k)$ , which is $(10-2)!$ or $8!$ . $8! = 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1$ .
Apply Combination Formula: Now we can plug these values into the combination formula: $C(10, 2) = \frac{10!}{(2!(10-2)!)} = \frac{10!}{(2! \times 8!)}$ .
Simplify Factorials: We simplify the factorials by canceling out the common terms in $10!$ and $8!$ . This leaves us with $\frac{10 \times 9}{2 \times 1}$ .
Perform Division: Now we perform the division: $\frac{(10 \times 9)}{(2 \times 1)} = \frac{90}{2} = 45$ .
Final Result: Therefore, there are $45$ different ways to cross $10$ distinct rice varieties with each other.

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