In how many ways can 2 students be selected from a group of 5 students in a debating competition?

  • A 25 ways
  • B 10 ways
  • C 15 ways
  • D 20 ways

The correct answer is B. 10 ways

To find the number of ways to select 2 students from a group of 5 students, we use the concept of combinations, often denoted as "n choose k" or \( C(n, k) \).

The formula for combinations is:

\(C(n, k) = \frac{n!}{k! \cdot (n - k)!} \)

where \( n \) is the total number of items (in this case, students), and \( k \) is the number of items to be chosen (in this case, 2).

Given \( n = 5 \) and \( k = 2 \), let's calculate:

\(C(5, 2) = \frac{5!}{2! \cdot (5 - 2)!} = \frac{5!}{2! \cdot 3!} \)

\(C(5, 2) = \frac{5 \cdot 4 \cdot 3 \cdot 2 \cdot 1}{(2 \cdot 1) \cdot (3 \cdot 2 \cdot 1)} = \frac{120}{12} = 10 \)

So, there are 10 ways to select 2 students from a group of 5 students.

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