Step-by-step explanation:
The number of black balls is
The number of red balls is
The total number of balls are
Step 1:
Calculate the numerator
The number of ways to choose 3 black from 8 black balls is given below as
We will then choose the remaining 2 red balls from the 7 red balls below as
Therefore,
The numerator will be
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
Therefore,
The probability of picking exactly 3 black balls will be
Hence,
The final answer is