5 apples are to be given to a group of children of 6 boys and 2girls. what is the probability that.
a particular boy david will receive an apple. ( answer provided 5/8) mind to show how
Hello, qweiop90!
5 apples are to be given to a group of children of 6 boys and 2girls.
What is the probability that a particular boy, David, will receive an apple.
Answer: .$\displaystyle \frac{5}{8}$
5 apples are given to 8 children; there are: .$\displaystyle {8\choose5} \:=\:{\color{blue}56}$ possible ways.
In how many ways can David be not given an apple?
Then the 5 apples are given to the other 5 boys and the 2 girls.
There are: .$\displaystyle {7\choose5} \:=\:21$ ways that David does not get an apple.
Hence, there are: .$\displaystyle 56 - 21 \:=\:{\color{blue}35}$ ways that David does get an apple.
Therefore: .$\displaystyle P(\text{David gets an apple}) \;=\;\frac{35}{56} \;=\;\frac{5}{8}$