Question 34 of 34intermediate🔍 AnalyzeEssay3 marks

Compare with your friends to find what other numbers they have made. See if all of you together can come up with all the 24 numbers. How do you know that you have all possible such numbers?

Correct Answer

Method: Systematic counting.

Calculation: With 4 different digits, the number of 4-digit numbers without repetition: 4×34 \times 3 × 2×12 \times 1 = 24

Organization: Fix each digit in the thousands place:

  • 6 numbers starting with 7
  • 6 numbers starting with 4
  • 6 numbers starting with 3
  • 6 numbers starting with 2

Conclusion: ∴ If we have exactly 24 unique numbers with no repetitions, we have all possible numbers.

Exercise: Let Us Explore | Q: 2 | (Page Page 23)
For More Understanding

Explanation

This activity encourages collaborative learning and systematic thinking. Students learn to verify completeness by using the fundamental counting principle: for a 4-digit number using 4 distinct digits, there are 4 choices for thousands, 3 for hundreds, 2 for tens, and 1 for ones place, giving 4×34 \times 3 × 2×12 \times 1 = 24 total possibilities.

Solution Steps

  1. Use systematic counting to verify completeness.

  2. Calculate total possibilities: 4×34 \times 3 × 2×12 \times 1 = 24

  3. Organize by fixing each digit in the thousands place.

  4. Verify exactly 24 unique numbers with no repetitions.

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