Fruits

In the shop sell 4 kinds of fruits. How many ways can we buy three pieces of fruit?

Result

x =  20

Solution:

C3(6)=(63)=6!3!(6−3)!=6⋅5⋅43⋅2⋅1=20 n=4 k=3  x=(n+k−1k)=(4+3−13)=20C_{{ 3}}(6) = \dbinom{ 6}{ 3} = \dfrac{ 6! }{ 3!(6-3)!} = \dfrac{ 6 \cdot 5 \cdot 4 } { 3 \cdot 2 \cdot 1 } = 20 \ \\ n=4 \ \\ k=3 \ \\ \ \\ x={ { n+k-1 } \choose k }={ { 4+3-1 } \choose 3 }=20

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