The Value of 9C3 | Understanding Combinations and Calculating 9C3 Mathematically

9C3

To find the value of 9C3, first let’s understand what it means

To find the value of 9C3, first let’s understand what it means. The notation 9C3 represents the number of ways to choose 3 items from a set of 9 items, also known as a combination.

The formula for combinations is given by:

nCr = n! / (r! * (n – r)!)

Here, n represents the total number of items in the set, and r represents the number of items to be chosen. The exclamation mark (!) denotes the factorial of a number, which means multiplying all the whole numbers from 1 to that number.

Now, let’s calculate 9C3 using the combination formula:

9C3 = 9! / (3! * (9 – 3)!)
= 9! / (3! * 6!)

To simplify this expression, we compute the factorials:

9! = 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1
3! = 3 * 2 * 1
6! = 6 * 5 * 4 * 3 * 2 * 1

Plugging these values back into the formula:

9C3 = (9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1) / ((3 * 2 * 1) * (6 * 5 * 4 * 3 * 2 * 1))

Simplifying the expression further:

9C3 = (9 * 8 * 7) / (3 * 2 * 1)
= 504 / 6
= 84

Therefore, 9C3 equals 84. This means that there are 84 different ways to choose 3 items from a set of 9 items.

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