# 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 many

3 −

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?

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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

## Question

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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 )

Download PDF Attempt Online

View all Allahabad High Court Group C Papers >

60 40 20 30

## Answer (Detailed Solution Below)

Option 1 : 60

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## Detailed Solution

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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.**

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