Question

How do you evaluate `""""_7C_4`?

Answer 1

`""^7C_4 = 35`

Explanation:

We evaluate combinations using definition:

`""^nC_r = ( (n), (r) ) = (n!)/( (n-r)! \ r!)`

Thus:

`""^7C_4 = (7!)/( (7-4)! \ 4!)`
`" " = (7!)/( 3! \ 4!)`
`" " = (1.2.3.4.5.6.7)/( (1.2.3) \ (1.2.3.4))`
`" " = (5.6.7)/( (1.2.3) )`
`" " = (5.7)`
`" " = 35`

Or we could evaluate by just comoputing thefactorial values

`""^7C_4 = = (7!)/( 3! \ 4!)`
`" " = (5040)/( 6 * 24)`
`" " = (5040)/( 144)`
`" " = 35`

Finally, most modern calculators have the ability to peform combination calculations via an `nCr` or `""^nC_r` button