Dekh bhen 4 favarable outcomes ayegi 

Given:
- The bag contains 5 apples and 3 oranges.
- 3 fruits are taken at the same time.

To find:
- The probability that at least 2 of them are apples.

Solution:

Step 1: Determine the total number of ways to choose 3 fruits from the bag.
The total number of fruits in the bag is 5 apples + 3 oranges = 8 fruits.
Therefore, the total number of ways to choose 3 fruits from the bag is given by the combination formula:
nCr = (n!)/(r!(n-r)!)
where n is the total number of fruits and r is the number of fruits to choose.

Using the combination formula, we have:
8C3 = (8!)/(3!(8-3)!)
= (8!)/(3!5!)
= (8 x 7 x 6 x 5!)/(3 x 2 x 1 x 5!)
= (8 x 7 x 6)/(3 x 2 x 1)
= 56

Therefore, there are a total of 56 ways to choose 3 fruits from the bag.

Step 2: Determine the number of ways to choose at least 2 apples.
To find the number of ways to choose at least 2 apples, we need to consider two cases:
1. Choosing exactly 2 apples and 1 orange.
2. Choosing all 3 apples.

Case 1: Choosing exactly 2 apples and 1 orange.
The number of ways to choose exactly 2 apples from 5 is given by the combination formula:
5C2 = (5!)/(2!(5-2)!)
= (5!)/(2!3!)
= (5 x 4 x 3!)/(2 x 1 x 3!)
= 10

The number of ways to choose 1 orange from 3 is given by the combination formula:
3C1 = (3!)/(1!(3-1)!)
= (3!)/(1!2!)
= (3 x 2!)/(1 x 2!)
= 3

Therefore, the number of ways to choose exactly 2 apples and 1 orange is 10 x 3 = 30.

Case 2: Choosing all 3 apples.
The number of ways to choose all 3 apples from 5 is given by the combination formula:
5C3 = (5!)/(3!(5-3)!)
= (5!)/(3!2!)
= (5 x 4 x 3!)/(3 x 2 x 1!)
= 10

Therefore, the number of ways to choose all 3 apples is 10.

Step 3: Calculate the probability.
The probability that at least 2 of the fruits are apples is the sum of the probabilities of the two cases divided by the total number of ways to choose 3 fruits.

Probability = (Number of ways to choose exactly 2 apples and 1 orange + Number of ways to choose all 3 apples) / Total number of ways to choose 3 fruits
Probability = (30 + 10) / 56
Probability = 40 / 56
Probability =