Question:
Let 5 digit numbers be constructed using the digits $0,2,3,4,7,9$ with repetition allowed, and are arranged in ascending order with serial numbers Then the serial number of the number 42923 is
Let 5 digit numbers be constructed using the digits $0,2,3,4,7,9$ with repetition allowed, and are arranged in ascending order with serial numbers Then the serial number of the number 42923 is
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When constructing numbers with restricted digits, organize them systematically to calculate the serial number efficiently. Use counting principles like combinations and arrange them in ascending order to avoid missing any possibilities.
Updated On: Mar 21, 2025
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Correct Answer: 2997
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Approach Solution -2
\[
2 + 3 + 4 + 6 + 6 = 1296
\]
\[
3 + 3 + 6 + 6 + 6 = 1296
\]
\[
40 + 6 + 6 = 216
\]
\[
420 + 6 = 36
\]
\[
422 + 6 = 36
\]
\[
423 + 6 = 36
\]
\[
424 + 6 = 36
\]
\[
427 + 6 = 36
\]
\[
429 + 6 = 6
\]
\[
429 + 20 = 6
\]
\[
429 22 = 1
\]
\[
429 23 = 1
\]
\[
= 2997
\]
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Concepts Used:
Permutations and Combinations
Permutation:
Permutation is the method or the act of arranging members of a set into an order or a sequence.
- In the process of rearranging the numbers, subsets of sets are created to determine all possible arrangement sequences of a single data point.
- A permutation is used in many events of daily life. It is used for a list of data where the data order matters.
Combination:
Combination is the method of forming subsets by selecting data from a larger set in a way that the selection order does not matter.
- Combination refers to the combination of about n things taken k at a time without any repetition.
- The combination is used for a group of data where the order of data does not matter.