Question 8 of 12intermediate🔧 ApplyNumerical3 marks

Suppose there are 10 students in your class. You want to select three out of them. How many samples are possible?

Correct Answer

The number of possible samples is 120.

Calculation:

Step 1: Identify the values - Total students (N) = 10, Students to be selected (n) = 3.

Step 2: Apply the combination formula for selecting samples: Number of samples = N! / [n! × (N-n)!]

Step 3: Substitute the values: = 10! / [3! × (10-3)!] = 10! / [3! × 7!]

Step 4: Simplify: = (10×910 \times 9 × 8) / (3×23 \times 2 × 1) = 720 / 6 = 120 samples

Therefore, 120 different samples of 3 students each can be formed from a class of 10 students.

Exercise: EXERCISES | Q: 10 | (Page 13)
For More Understanding

Explanation

This question tests the understanding of combinations in sampling. When selecting a random sample where order doesn't matter (as in selecting students), we use combinations. The formula N! / [n! × (N-n)!] calculates all possible ways to select n items from N items. This concept is fundamental to understanding random sampling methods like the lottery method mentioned in the chapter.

Solution Steps

  1. Step 1: Identify N = 10 students, n = 3 students to select

  2. Step 2: Use combination formula: N! / [n! × (N-n)!]

  3. Step 3: Calculate: 10! / [3! × 7!] = (10×910 \times 9 × 8) / (3×23 \times 2 × 1)

  4. Step 4: Solve: 720 / 6 = 120 possible samples

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