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NCERT Solutions for Class 4th Maths Chapter 4 Four-digit numbers from 2, 3, 4, 7 — Let Us Explore

Book page 61 Updated on2026-09-19

Q1.
1. 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.
Answer

Work in a fixed order so that nothing is missed. Take each digit in turn as the Thousands digit, largest first.

Thousands digitThe six numbers (decreasing)
77432  7423  7342  7324  7243  7234
44732  4723  4372  4327  4273  4237
33742  3724  3472  3427  3274  3247
22743  2734  2473  2437  2374  2347
All 24 numbers in decreasing order:
7432  7423  7342  7324  7243  7234
4732  4723  4372  4327  4273  4237
3742  3724  3472  3427  3274  3247
2743  2734  2473  2437  2374  2347
Why it happens: the largest number starts with the largest digit. Inside each group we again put the largest remaining digit first.
Q2.
2. 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?
Answer

Sample answer: our group put all our lists side by side, struck off the repeats and found that we had all 24 numbers together.

Here is how we know 24 is the full count.

  1. The Thousands place can be filled in 4 ways (2, 3, 4 or 7).
  2. Now one digit is used up, so the Hundreds place can be filled in 3 ways.
  3. The Tens place can then be filled in 2 ways.
  4. The last digit has only 1 place left to go.
4 × 3 × 2 × 1 = 24
Why it happens: working in this fixed order — 7…, then 4…, then 3…, then 2… — gives 6 numbers in each group, and 6 + 6 + 6 + 6 = 24. No number can be missed and none can be repeated.
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