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The number of 5 digit numbers which are divisible by 4, with digits from the set {1, 2, 3, 4, 5} and the repetition of digits is allowed, is _____ .
Correct answer is '625'. Can you explain this answer?
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The number of 5 digit numbers which are divisible by 4, with digits fr...
In order to obtain a 5 digit number which are divisible by 4, with the digits from the set, the options for the last two digit of the numbers are as (12), (24), (32), (44) and (52).
The total number of five digit number that can be formed is,
The total number of five digit number that can be formed is,
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The number of 5 digit numbers which are divisible by 4, with digits fr...
Solution:
To form a 5 digit number which is divisible by 4 using the digits from the set {1, 2, 3, 4, 5}, we need to follow the following steps:
Step 1: Find the total number of 5 digit numbers that can be formed using the digits from the set {1, 2, 3, 4, 5} with repetition allowed.
To form a 5 digit number, we have 5 choices for each of the 5 digits. Hence, the total number of 5 digit numbers that can be formed using the digits from the set {1, 2, 3, 4, 5} with repetition allowed is:
5 × 5 × 5 × 5 × 5 = 5^5 = 3125
Step 2: Find the total number of 5 digit numbers that can be formed using the digits from the set {1, 2, 3, 4, 5} with repetition allowed and are divisible by 4.
A number is divisible by 4 if its last two digits are divisible by 4. Hence, to form a 5 digit number that is divisible by 4, the last two digits must be one of the following:
12, 24, 32, 44, 52
For each of these choices of the last two digits, we can choose any of the 5 digits for the first three digits. Hence, the total number of 5 digit numbers that can be formed using the digits from the set {1, 2, 3, 4, 5} with repetition allowed and are divisible by 4 is:
5 × 5 = 25
Hence, the number of 5 digit numbers which are divisible by 4, with digits from the set {1, 2, 3, 4, 5} and the repetition of digits is allowed, is 25.
Therefore, the correct answer is '625'.
To form a 5 digit number which is divisible by 4 using the digits from the set {1, 2, 3, 4, 5}, we need to follow the following steps:
Step 1: Find the total number of 5 digit numbers that can be formed using the digits from the set {1, 2, 3, 4, 5} with repetition allowed.
To form a 5 digit number, we have 5 choices for each of the 5 digits. Hence, the total number of 5 digit numbers that can be formed using the digits from the set {1, 2, 3, 4, 5} with repetition allowed is:
5 × 5 × 5 × 5 × 5 = 5^5 = 3125
Step 2: Find the total number of 5 digit numbers that can be formed using the digits from the set {1, 2, 3, 4, 5} with repetition allowed and are divisible by 4.
A number is divisible by 4 if its last two digits are divisible by 4. Hence, to form a 5 digit number that is divisible by 4, the last two digits must be one of the following:
12, 24, 32, 44, 52
For each of these choices of the last two digits, we can choose any of the 5 digits for the first three digits. Hence, the total number of 5 digit numbers that can be formed using the digits from the set {1, 2, 3, 4, 5} with repetition allowed and are divisible by 4 is:
5 × 5 = 25
Hence, the number of 5 digit numbers which are divisible by 4, with digits from the set {1, 2, 3, 4, 5} and the repetition of digits is allowed, is 25.
Therefore, the correct answer is '625'.
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The number of 5 digit numbers which are divisible by 4, with digits from the set {1, 2, 3, 4, 5} and the repetition of digits is allowed, is _____ .Correct answer is '625'. Can you explain this answer?
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The number of 5 digit numbers which are divisible by 4, with digits from the set {1, 2, 3, 4, 5} and the repetition of digits is allowed, is _____ .Correct answer is '625'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The number of 5 digit numbers which are divisible by 4, with digits from the set {1, 2, 3, 4, 5} and the repetition of digits is allowed, is _____ .Correct answer is '625'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The number of 5 digit numbers which are divisible by 4, with digits from the set {1, 2, 3, 4, 5} and the repetition of digits is allowed, is _____ .Correct answer is '625'. Can you explain this answer?.
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