Divide

How many different ways can three people divide 7 pears and 5 apples?

Result

x =  2940

Solution:

C3(9)=(93)=9!3!(9−3)!=9⋅8⋅73⋅2⋅1=84 n1=7 n2=5 k=3 C3(7)=(73)=7!3!(7−3)!=7⋅6⋅53⋅2⋅1=35  x=(n1+k−1k)⋅ (n2+k−1k)=(7+3−13)⋅ (5+3−13)=2940C_{{ 3}}(9) = \dbinom{ 9}{ 3} = \dfrac{ 9! }{ 3!(9-3)!} = \dfrac{ 9 \cdot 8 \cdot 7 } { 3 \cdot 2 \cdot 1 } = 84 \ \\ n_{1}=7 \ \\ n_{2}=5 \ \\ k=3 \ \\ C_{{ 3}}(7)=\dbinom{ 7}{ 3}=\dfrac{ 7! }{ 3!(7-3)!}=\dfrac{ 7 \cdot 6 \cdot 5 } { 3 \cdot 2 \cdot 1 }=35 \ \\ \ \\ x={ { n_{1}+k-1 } \choose k } \cdot \ { { n_{2}+k-1 } \choose k }={ { 7+3-1 } \choose 3 } \cdot \ { { 5+3-1 } \choose 3 }=2940

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Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...):

Showing 3 comments:
#
Math student
I think that you mixed up n and k. My understanding is that : n = 3, k1 = 7, k2 = 5

2 months ago  1 Like
#
Math student
shouldn't it be (7 2) and (9 2)?

1 month ago  1 Like
#
Leilani Sue
Why are (7 3) and (9 3) being multiplied?

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