Question 33 of 34advanced✨ CreateShort Answer5 marks

Make as many four-digit numbers as possible using the digits 2, 3, 4, 7 without repetition. There are 24 different numbers possible. Find as many as you can and arrange the numbers in decreasing order in your notebook.

Correct Answer

Total numbers possible: 4×34 \times 3 × 2×12 \times 1 = 24 numbers

Step 1: Start with largest digit 7 in thousands place: 7432, 7423, 7342, 7324, 7243, 7234

Step 2: Next with 4 in thousands: 4732, 4723, 4372, 4327, 4273, 4237

Step 3: Next with 3 in thousands: 3742, 3724, 3472, 3427, 3274, 3247

Step 4: Finally with 2 in thousands: 2743, 2734, 2473, 2437, 2374, 2347

Step 5: Arrange all in decreasing order

Answer: 7432, 7423, 7342, 7324, 7243, 7234, 4732, 4723, 4372, 4327, 4273, 4237, 3742, 3724, 3472, 3427, 3274, 3247, 2743, 2734, 2473, 2437, 2374, 2347

Exercise: Let Us Explore | Q: 1 | (Page Page 23)
For More Understanding

Explanation

Using 4 different digits, we can make 4×34 \times 3 × 2×12 \times 1 = 24 different four-digit numbers. Starting with 7 in thousands place gives 6 numbers, starting with 4 gives 6 numbers, starting with 3 gives 6 numbers, and starting with 2 gives 6 numbers. Arranging in decreasing order means starting with the largest number.

Solution Steps

  1. Step 1: Start with largest digit 7 in thousands place: 7432, 7423, 7342, 7324, 7243, 7234

  2. Step 2: Next with 4 in thousands: 4732, 4723, 4372, 4327, 4273, 4237

  3. Step 3: Next with 3 in thousands: 3742, 3724, 3472, 3427, 3274, 3247

  4. Step 4: Finally with 2 in thousands: 2743, 2734, 2473, 2437, 2374, 2347

  5. Step 5: Arrange all in decreasing order

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