What is the result of calculating 6C4?

To calculate 6C4, which represents the number of combinations of 6 items taken 4 at a time, you can use the combination formula:

[ nCk = \frac{n!}{k!(n-k)!}

]

In this case, ( n = 6 ) and ( k = 4 ). Plugging in these values:

[ 6C4 = \frac{6!}{4!(6-4)!} = \frac{6!}{4! \cdot 2!} ]

Now, calculating the factorials:

• ( 6! = 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 720 )
• ( 4! = 4 \times 3 \times 2 \times 1 = 24 )
• ( 2! = 2 \times 1 = 2 )

Substituting these into the formula:

[ 6C4 = \frac{720}{24 \times 2} = \frac{720}{48} = 15 ]

Thus, the correct answer is indeed 15, which corresponds to the choice provided