Explanation:
The number of black balls is
[tex]n(B)=8[/tex]
The number of red balls is
[tex]n(R)=7[/tex]
The total number of balls are
[tex]totalballs=8+7=15[/tex]
Step 1:
Calculate the numerator
The number of ways to choose 3 black from 8 black balls is given below as
[tex]\begin{gathered} 8C3 \\ =56ways \end{gathered}[/tex]
We will then choose the remaining 2 red balls from the 7 red balls below as
[tex]\begin{gathered} 7C2 \\ 21ways \end{gathered}[/tex]
Therefore,
The numerator will be
[tex]\begin{gathered} 56\times21 \\ =1176 \end{gathered}[/tex]
Step 2:
Calculate the denominator
Here we are going to calculate the number of ways to choose 5 balls from a total of 15 balls below as
[tex]\begin{gathered} 15C5 \\ =3003 \end{gathered}[/tex]
Therefore,
The probability of picking exactly 3 black balls will be
[tex]\begin{gathered} \frac{1176}{3003} \\ \frac{56}{143} \end{gathered}[/tex]
Hence,
The final answer is
[tex]\Rightarrow\frac{56}{143}[/tex]
