Twelve flowers

A florist has roses, tulips, daffodils, and carnations to use in flower arrangements. If she were to make an arrangement using 12 flowers, how many different combinations of these 4 types of flowers would be possible?


x =  455


C12(15)=(1512)=15!12!(1512)!=151413321=455 n=4 k=12  x=(n+k1k)=(4+12112)=455C_{{ 12}}(15) = \dbinom{ 15}{ 12} = \dfrac{ 15! }{ 12!(15-12)!} = \dfrac{ 15 \cdot 14 \cdot 13 } { 3 \cdot 2 \cdot 1 } = 455 \ \\ n=4 \ \\ k=12 \ \\ \ \\ x={ { n+k-1 } \choose k }={ { 4+12-1 } \choose 12 }=455

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