Question

Find the value of the combination. 10C2

Answer 1

10C2 represents the number of ways to choose 2 items from 10 distinct items, calculated as 10! / (2! * 8!) which simplifies to 45. There are 45 ways to choose 2 items from a set of 10.

Step-by-step explanation:

The combination 10C2 refers to the number of ways to choose 2 items from a set of 10 distinct items, without regard for order. This is calculated using the formula for combinations which is nCr = n! / [r! * (n-r)!].

Let's break it down:

1. n! is the factorial of n and means the product of all positive integers up to n.
2. r! is the factorial of r.
3. (n-r)! is the factorial of the difference between n and r.

For 10C2:

• First calculate 10!, which is 10 x 9 x 8 x ... x 2 x 1.
• Then calculate 2!, which is 2 x 1.
• Also calculate (10-2)!, which is 8!.
• Applying the formula, we get 10C2 = 10! / (2! * 8!), which simplifies to (10 x 9) / (2 x 1).
• After cancellation and simplification, the result is 45.

Thus, there are 45 ways to choose 2 items from a set of 10.

Answer 2

The combination 10C2 represents the number of ways to choose 2 items from 10 without considering the order. Using the formula n! / (r! * (n-r)!), one can calculate it by simplifying 10! / (2! * 8!) to obtain the value 45.

Step-by-step explanation:

The combination formula, often represented as nCr, refers to the number of ways to choose r items from a set of n without regard to order. To compute 10C2, which means selecting 2 items from a set of 10, you can apply the combination formula n! / (r! * (n-r)!).

Let's break it down step-by-step:

1. Compute 10! (10 factorial), which is 10 × 9 × 8 × ... × 1.
2. Compute 2! (2 factorial), which is simply 2 × 1.
3. Compute (10-2)! which is 8! (8 factorial).
4. Now, substitute into the formula: 10! / (2! × 8!) = (10 × 9) / (2 × 1) since the terms from 8! cancel out the corresponding terms in 10!.
5. Finally, calculate the result: (10 × 9) / (2 × 1) = 90 / 2 = 45.

Therefore, the value of 10C2 is 45.