# Bouquets

In the flower shop they sell roses, tulips and daffodils. How many different bouquets of 5 flowers can we made?

Result

x =  21

#### Solution:

$C_{{ 5}}(7) = \dbinom{ 7}{ 5} = \dfrac{ 7! }{ 5!(7-5)!} = \dfrac{ 7 \cdot 6 } { 2 \cdot 1 } = 21 \ \\ n=3 \ \\ k=5 \ \\ \ \\ x={ { n+k-1 } \choose k }={ { 3+5-1 } \choose 5 }=21$

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