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

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

• A. 4C2 = 4
• B. 4C2 = 6
• C. 4C2 = 8
• D. 4C2 = 10

Answer: (B)

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

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