How do you calculate the total number of combinations when choosing 2 items from a set of 4?

To find the total number of combinations when choosing 2 items from a set of 4, you use the combination formula, which is given by the formula:

[

nCr = \frac{n!}{r!(n-r)!}

]

In this case, ( n = 4 ) (the total number of items) and ( r = 2 ) (the number of items to choose).

Substituting the values into the formula:

[

4C2 = \frac{4!}{2!(4-2)!}

]

This can be simplified further:

1. Calculate the factorials:

• ( 4! = 4 \times 3 \times 2 \times 1 = 24 )

• ( 2! = 2 \times 1 = 2 )

• ( (4-2)! = 2! = 2 )

2. Substitute these values back into the formula:

[

4C2 = \frac{24}{2 \times 2} = \frac{24}{4} = 6

]

This calculation reveals that the total number of combinations of choosing 2 items from a set of