Divide

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

Correct answer:

x =  756

Step-by-step explanation:

$$\begin{gathered} C_2(9)=\left({\displaystyle \genfrac{}{}{0px}{}{9}{2}}\right)={\displaystyle \frac{9!}{2!(9-2)!}}={\displaystyle \frac{9\cdot 8}{2\cdot 1}}=36 \\ {n}_1=7 \\ {n}_2=5 \\ k=3-1=2 \\ {C}_2(7)=\left({\displaystyle \genfrac{}{}{0px}{}{7}{2}}\right)={\displaystyle \frac{7!}{2!(7-2)!}}={\displaystyle \frac{7\cdot 6}{2\cdot 1}}=21 \\ {x}_1=\left(\genfrac{}{}{0px}{}{n_1+k}{k}\right)=\left(\genfrac{}{}{0px}{}{7+2}{2}\right)=36 \\ {x}_2=\left(\genfrac{}{}{0px}{}{n_2+k}{k}\right)=\left(\genfrac{}{}{0px}{}{5+2}{2}\right)=21 \\ x=x_1\cdot x_2=36\cdot 21=756 \end{gathered}$$

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Showing 5 comments:

Math student

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

1 year ago  1 Like Like

Math student

shouldn't it be (7 2) and (9 2)?

1 year ago  1 Like Like

Leilani Sue

Why are (7 3) and (9 3) being multiplied?

1 year ago  Like

Zs+ucitel

its 9 choose 3.... its combinations with repetions - and use formula

11 months ago  Like

Zs+ucitel

Number of ways of dividing 'n' identical objects into 'r' groups such that each group can contain any number of objects is given by:

C( n+k-1,k-1)

11 months ago  Like

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