# Combinatorics

The city has 7 fountains. Works only 6. How many options are there that can squirt ?

Result

n =  7

#### Solution:

$C_{{ 6}}(7) = \dbinom{ 7}{ 6} = \dfrac{ 7! }{ 6!(7-6)!} = \dfrac{ 7 } { 1 } = 7 \ \\ n={ { 6 } \choose 7 }=7$

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