how do you calculate combinations [C(6,2)] without using a calculator. I know that this is supposed to be a case of choosing 2 of six objects, but I'm notfamiliar with the logic behind it. can you help, please?

It's actually 6 choose 2 objects
The definition of nCr or n choose r is
(1) n!/(r!(n-r)!)
Here n=6 and r=2 so we have 6!/(2!*(6-2)!)= (6*5*4!)/(2!*4!)= 6*5/2! = 3*5=15
The formula (1) is what you should remember here.

25

To calculate combinations without using a calculator, you can use the formula for combinations, which is nCr = n! / (r! * (n - r)!), where n is the total number of objects and r is the number of objects you want to choose.

In this case, you want to calculate C(6,2), which means choosing 2 objects out of a total of 6 objects.

So, using the formula, you can calculate it step by step:

1. First, calculate the factorial of 6, denoted as 6!. This means multiplying all the numbers from 6 down to 1. So, 6! = 6 * 5 * 4 * 3 * 2 * 1 = 720.

2. Next, calculate the factorial of 2, denoted as 2!. This means multiplying all the numbers from 2 down to 1. So, 2! = 2 * 1 = 2.

3. Calculate the factorial of (6 - 2), denoted as (6 - 2)! or 4!. This means multiplying all the numbers from 4 down to 1. So, 4! = 4 * 3 * 2 * 1 = 24.

Now, substitute these values into the formula:

nCr = 6! / (2! * (6 - 2)!)
= 720 / (2 * 24)
= 720 / 48
= 15.

Therefore, C(6,2) = 15, which means there are 15 different ways to choose 2 objects out of a set of 6 objects.