Question

I have $8$ pieces of strawberry candy (all identical) and $7$ pieces of rhubarb candy (all identical). Find the number of ways I can distribute this candy to $5$ children.

Answer 1

SOLUTION

GIVEN

I have 8 pieces of strawberry candy (all identical) and 7 pieces of rhubarb candy (all identical).

TO DETERMINE

The number of ways I can distribute this candy to 5 children.

EVALUATION

Number of strawberry candy = 8

Number of children = 5

The number of ways it can be distributed

$\sf{ = {}^{8}C_5 }$

$\displaystyle \sf{ = \frac{8!}{5!(8 - 5)!} }$

$\displaystyle \sf{ = \frac{8!}{5!3!} }$

$\displaystyle \sf{ = \frac{8 \times 7 \times 6 \times 5!}{5! \times 3 \times 2 \times 1} }$

$\displaystyle \sf{ = \frac{8 \times 7 \times 6 }{ 3 \times 2} }$

$\displaystyle \sf{ = 56 }$

Number of rhubarb candy = 7

Number of children = 5

The number of ways it can be distributed

$\sf{ = {}^{7}C_5 }$

$\displaystyle \sf{ = \frac{7!}{5!(7 - 5)!} }$

$\displaystyle \sf{ = \frac{7!}{5!2!} }$

$\displaystyle \sf{ = \frac{7 \times 6 \times 5!}{5! \times 2 \times 1} }$

$\displaystyle \sf{ = \frac{7 \times 6 }{ 2 \times 1} }$

$\displaystyle \sf{ = 21 }$

Hence the required number of ways these candies can be distributed to 5 children

= 56 + 21

= 77

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