if you have 6 books how many groups of four different books can you make out of the six?

If we assume that the order we choose those four books doesn't matter then it is
nCr=
6!/(2!4!)
= ?

Isn't it 6*6*6*6???

No, it is not 6*6*6*6. The reason is that when selecting groups of four different books, the order in which you choose them does not matter. In other words, if you select books A, B, C, and D, it is the same as selecting books B, C, D, and A. So, in this case, we are looking at combinations, not permutations.

To calculate the number of combinations, we use the formula for combination:

nCr = n! / (r!(n-r)!)

Where n is the total number of items and r is the number of items being chosen.

In this case, we have 6 books and we want to select groups of 4, so the calculation looks like this:

6C4 = 6! / (4!(6-4)!)
= 6! / (4!2!)

Using the factorial notation (!):

6! = 6 * 5 * 4 * 3 * 2 * 1
4! = 4 * 3 * 2 * 1
2! = 2 * 1

Plugging in the values:

6C4 = (6 * 5 * 4 * 3 * 2 * 1) / ((4 * 3 * 2 * 1) * (2 * 1))
= (6 * 5) / (2 * 1)
= 30 / 2
= 15

Therefore, you can make 15 groups of four different books out of the six.