how many 3-digit even numbers can be made using the digits 1, 2, 3, 4, 6, 7, if no digit is repeated?
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How many 3-digit even numbers can be made using the digits 1,2,3,4,6,7 if no digit is repeated?
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Updated on : 2022-09-05
A three digit even number is to be formed from given 6 digits 1,2,3,4,6,7.Solution Verified by Toppr □□□ HTO
Since, for the number is to be even , so ones place can be filled by 2,4 or 6. So, there are 3 ways to fill ones place.
Since, repetition is not allowed , so tens place can be filled by remaining 5 digits. So, tens place can be filled in 5 ways.
Similarly, hundred's place can be filled by remaining 4 digits. So, hundred's place can be filled in 4 ways.
So,required number of ways in which three digit even numbers can be formed from the given digits is 4×5×3=60
Alternative Method:3-digit even numbers are to be formed using the given six digits, ,2,3,4,6 and 7, without repeating the digits.
Then, units digits can be filled in 3 ways by any of the digits, 2,4 or 6.
Since the digits cannot be repeated in the 3-digit numbers and units place is already occupied with a digit (which is even), the hundreds and tens place is to be filled by the remaining 5 digits.
Therefore, the number of ways in which hundreds and tens place can be filled with the remaining 5 digits Is the permutation of 5 different digits taken 2 at a time.
5 P 2 = (5−2)! 5! = 3! 5!
Number of ways of filling hundreds and tens place
= 3! 5×4×3! =20
Thus, by multiplication principle, the required number of 3-digit numbers is 3×20=60
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How many 3 digit even numbers can be made using the digits 1,2,3,4,6,7 if no digit is repeated?
How many 3 digit even numbers can be made using the digits 1,2,3,4,6,7 if no digit is repeated?
Byju's Answer Standard XI Mathematics
Permutation: n Different Things Taken r at a Time
How many 3-di... Question
How many 3-digit even numbers can be made using the digits 1,2,3,4,6,7 if no digit is repeated?
Open in App Solution
Here, total number of digits = 6
The unit place can be filled with any one of the digits 2, 4, 6.
So number of permutation =
3 P 1 = 3 ! 2 ! = 3
Now, the tens and hundreds place can be filled by remaining 5 digits.
So number of permutations =
5 P 2 = 5 ! 3 ! = 5 × 4 × 3 ! 3 ! = 20
Hence total number of permutations =
3 × 20 = 60. Suggest Corrections 61
SIMILAR QUESTIONS
Q. How many3 −
digit even numbers can be made using the digits
1 , 2 , 3 , 4 , 6 , 7 ,
if no digit is repeated?
Q. how many 3 digit even numbers can be made using the digits 1 ,2, 3, 4 ,6 ,7 of no digit is repeated?RELATED VIDEOS
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Permutation: n Different Things Taken r at a Time
Standard XI Mathematics
[Solved] How many 3
Calculations: A three-digit even number is to be formed from given 6 digits 1, 2, 3, 4, 6, 7 The number at one's place can be filled by 2, 4, 6.
Home Quantitative Aptitude Permutation and Combination
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How many 3-digit even numbers can be formed using 1, 2, 3, 4, 6, 7 digits without repeating them?
This question was previously asked in
Allahabad High Court Group C Official Paper ( Held On : 20 Jan 2019 )
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View all Allahabad High Court Group C Papers >
60 40 20 30
Answer (Detailed Solution Below)
Option 1 : 60
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Calculations:A three-digit even number is to be formed from given 6 digits 1, 2, 3, 4, 6, 7
The number at one's place can be filled by 2, 4, 6.
Since repetition is not allowed
Now, Tens place can be filled by the remaining 5 digits
So, Tens place can be filled in 5 ways
Similarly, Hundred place can be filled by the remaining 4 digits
So, Hundred place can be filled in 4 ways
So, the Required number of ways in which three-digit even numbers can be formed from the given digits is
⇒ Number of ways = 5 × 4 × 3
⇒ Number of ways = 60
∴ The required number of ways formed using 3- digit even number using 1, 2, 3, 4, 6, 7 is 60.Download Solution PDF
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