Question:
How many different five digit numbers which are divisible by \(4\) can be formed using the digits in the number \(22457\) ?
How many different five digit numbers which are divisible by \(4\) can be formed using the digits in the number \(22457\) ?
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A number is divisible by 4 if its last two digits form a multiple of 4, so list the valid endings first.
Updated On: Nov 12, 2026
- \(60\)
- \(12\)
- \(54\)
- \(18\)
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Verified By Collegedunia
The Correct Option is D
Solution and Explanation
Step 1: Understanding the Concept
Digits available: 2, 2, 4, 5, 7. A number is divisible by 4 if the number formed by its last two digits is divisible by 4.
Step 2: Valid endings
Possible endings from these digits that are multiples of 4: 24, 52 and 72. (22, 42, 54, 74, 44 and so on are not multiples of 4.)
Step 3: Count for each ending
Ending 24: remaining digits 2, 5, 7 can be arranged in \(3!=6\) ways.
Ending 52: remaining 2, 4, 7 give \(3!=6\) ways.
Ending 72: remaining 2, 4, 5 give \(3!=6\) ways.
Step 4: Total
\(6+6+6=18\)
Final Answer:
There are 18 such numbers. \[ \boxed{\text{(D) }18} \]
Digits available: 2, 2, 4, 5, 7. A number is divisible by 4 if the number formed by its last two digits is divisible by 4.
Step 2: Valid endings
Possible endings from these digits that are multiples of 4: 24, 52 and 72. (22, 42, 54, 74, 44 and so on are not multiples of 4.)
Step 3: Count for each ending
Ending 24: remaining digits 2, 5, 7 can be arranged in \(3!=6\) ways.
Ending 52: remaining 2, 4, 7 give \(3!=6\) ways.
Ending 72: remaining 2, 4, 5 give \(3!=6\) ways.
Step 4: Total
\(6+6+6=18\)
Final Answer:
There are 18 such numbers. \[ \boxed{\text{(D) }18} \]
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