Answer:
340 ways
Step-by-step explanation:
Given:
Total number of oranges = 60
Number of rotten oranges = 4
Number of oranges picked = 3
Now, number of good oranges = Total number - Rotten oranges
= 60 - 4 = 56
Now, we need to pick at least two rotten oranges.
So, the possible outcomes can be as follows:
- 2 rotten oranges + 1 good orange = 3 oranges
- 3 rotten oranges + 0 good orange = 3 oranges
Now, number of ways of picking 'r' distinct objects from a total of 'n' objects is given as:
Now, picking 2 rotten oranges from a total of 4 rotten oranges is:
Similarly, picking 3 rotten oranges from a total of 4 rotten oranges is:
Now, picking 1 good orange from a total of 56 good oranges is:
Picking 0 good oranges means picking no good oranges.
Therefore, the total number of ways of picking at least 2 rotten oranges is the sum of the above two possibilities and is given as:
At least 2 rotten out of 3 picked = (2 rotten and 1 good) or 3 rotten
= 6 × 56 + 4
= 336 + 4 = 340 ways
Therefore, there are 340 ways of picking at least 2 rotten oranges when 3 oranges are picked from a total of 60 oranges.
