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A four digits number is formed by using only the digits 1,2 and 3 such that both 2and 3 appear at least once. The number of all such four digit number is?
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A four digits number is formed by using only the digits 1,2 and 3 such...
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Formulation of the problem:
To form a four-digit number using only the digits 1, 2, and 3 such that both 2 and 3 appear at least once.
Step 1: Total number of four-digit numbers:
There are 3 options for the first digit (1, 2, or 3) and 3 options for each of the remaining three digits. Therefore, the total number of four-digit numbers that can be formed is 3 x 3 x 3 x 3 = 81.
Step 2: Number of four-digit numbers without 2 or 3:
If 2 and 3 do not appear in the four-digit number, then there are only 1 option for each digit, which is 1. Therefore, the number of four-digit numbers without 2 or 3 is 1 x 1 x 1 x 1 = 1.
Step 3: Number of four-digit numbers with at least one 2 or 3:
To find the number of four-digit numbers with at least one 2 or 3, we subtract the number of four-digit numbers without 2 or 3 from the total number of four-digit numbers:
Number of four-digit numbers with at least one 2 or 3 = Total number of four-digit numbers - Number of four-digit numbers without 2 or 3
= 81 - 1
= 80.
Therefore, there are 80 four-digit numbers that can be formed using only the digits 1, 2, and 3 such that both 2 and 3 appear at least once.
Formulation of the problem:
To form a four-digit number using only the digits 1, 2, and 3 such that both 2 and 3 appear at least once.
Step 1: Total number of four-digit numbers:
There are 3 options for the first digit (1, 2, or 3) and 3 options for each of the remaining three digits. Therefore, the total number of four-digit numbers that can be formed is 3 x 3 x 3 x 3 = 81.
Step 2: Number of four-digit numbers without 2 or 3:
If 2 and 3 do not appear in the four-digit number, then there are only 1 option for each digit, which is 1. Therefore, the number of four-digit numbers without 2 or 3 is 1 x 1 x 1 x 1 = 1.
Step 3: Number of four-digit numbers with at least one 2 or 3:
To find the number of four-digit numbers with at least one 2 or 3, we subtract the number of four-digit numbers without 2 or 3 from the total number of four-digit numbers:
Number of four-digit numbers with at least one 2 or 3 = Total number of four-digit numbers - Number of four-digit numbers without 2 or 3
= 81 - 1
= 80.
Therefore, there are 80 four-digit numbers that can be formed using only the digits 1, 2, and 3 such that both 2 and 3 appear at least once.
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A four digits number is formed by using only the digits 1,2 and 3 such that both 2and 3 appear at least once. The number of all such four digit number is?
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A four digits number is formed by using only the digits 1,2 and 3 such that both 2and 3 appear at least once. The number of all such four digit number is? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A four digits number is formed by using only the digits 1,2 and 3 such that both 2and 3 appear at least once. The number of all such four digit number is? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A four digits number is formed by using only the digits 1,2 and 3 such that both 2and 3 appear at least once. The number of all such four digit number is?.
A four digits number is formed by using only the digits 1,2 and 3 such that both 2and 3 appear at least once. The number of all such four digit number is? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A four digits number is formed by using only the digits 1,2 and 3 such that both 2and 3 appear at least once. The number of all such four digit number is? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A four digits number is formed by using only the digits 1,2 and 3 such that both 2and 3 appear at least once. The number of all such four digit number is?.
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