Q. Three individuals have to be selected from a group of 6 people. How many different combinations are possible?

Correct Answer: (C) 20

Explanation:

To solve this problem, we need to calculate the number of combinations of selecting 3 individuals from a group of 6 people. The formula for combinations is:

nCr = n! / [r!(n – r)!]

Where:
– n is the total number of items (6 in this case),
– r is the number of items to choose (3 in this case),
– ! denotes factorial (e.g., 3! = 3 × 2 × 1 = 6).

Substitute the values into the formula:

6C3 = 6! / [3!(6 – 3)!]

Simplify step by step:
1. 6! = 6 × 5 × 4 × 3 × 2 × 1 = 720
2. 3! = 3 × 2 × 1 = 6
3. (6 – 3)! = 3! = 6

Now substitute these values into the formula:

6C3 = 720 / (6 × 6) = 720 / 36 = 20

Thus, the number of combinations is 20.

Correct Answer: (C) 20