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Find the number of three digit numbers that are divisible by 2

Question

Find the number of three digit numbers that are divisible by $2$ but not divisible by $6$ and are formed with the digits $1, 2, 3, 4, 6$ when repetition is not allowed

10

12

20

25

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Levi Discussed

Find the number of three digit numbers that are divisible by

2

but not divisible by

6

and are formed with the digits

1, 2, 3, 4, 6

when repetition is not allowed

15 mins ago

Discuss this question LIVE

15 mins ago

Text solutionVerified

A number is divisible by

2

if the last digit is an even number

A number is divisible by

6

if it is divisible by both

2

and

3

So, a three digit number formed

1, 2, 3, 4, 6

is divisible by

2

if the last digits are

2, 4

6

And it is not divisible by

6

if it is not divisible by

3

So, we need to find numbers divisible by

2

and not by

3

with no repetition

Case 1 :

(1, 4) (3, 6)

\Rightarrow

Number of possiblities

= (2!) 2

Case 2 :

(1, 2) (1, 3) (1, 6) (3, 6)

Number of Possiblities

= (2!) 4

Case 3 :

(1, 3) (1, 4) (2, 3) (3, 4)

Number of Possiblities

= (2!) 4

Hence the correct answer is

20

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Question Text	Find the number of three digit numbers that are divisible by $2$ but not divisible by $6$ and are formed with the digits $1, 2, 3, 4, 6$ when repetition is not allowed
Answer Type	Text solution:1
Upvotes	150

Find the number of three digit numbers that are divisible by 2 but not divisible by 6 and are formed with the digits 1,2,3,4,6 when repetition is not allowed

Text solutionVerified

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Find the number of three digit numbers that are divisible by $2$ but not divisible by $6$ and are formed with the digits $1, 2, 3, 4, 6$ when repetition is not allowed