Question

Evaluate.C15 3 It says I need to evaluate 15^C 3

Answer 1

Explanation

We are required to determine the value of the following:

`_(15)C_3`

This is achieved thus:

We know that the combination formula is given as:

Therefore, we have:

`\begin{gathered} _(15)C_3=(15!)/(3!(15-3)!) \\ _(15)C_3=(15!)/(3!12!) \\ _(15)C_3=(15\cdot14\cdot13\cdot12!)/(3!12!) \\ _(15)C_3=(15\cdot14\cdot13)/(3!)=(15\cdot14\cdot13)/(3\cdot2\cdot1) \\ _(15)C_3=5\cdot7\cdot13 \\ _(15)C_3=455 \end{gathered}`

Hence, the answer is:

`455`