Question

Evaluate the expression express your answer in exact simplest form12C3=

Answer 1

Given:

`_(12)C_3`

Find-: Evaluate the expression.

Sol:

Formula:

`_nC_r=(n!)/(r!(n-r)!)`

So the value is:

`_(12)C_3=(12!)/(3!(12-3)!)`
`\begin{gathered} =(12!)/(3!(12-3)!) \\ \\ =(12*11*10*9!)/(3!*9!) \\ \\ =(12*11*10)/(3!) \end{gathered}`

value is:

`\begin{gathered} =(12*11*10)/(3!) \\ \\ =(12*11*10)/(3*2*1) \\ \\ =(12*11*10)/(6) \\ \\ =2*11*10 \\ \\ =22*10 \\ \\ =220 \end{gathered}`

So the value is 220.