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Find the member of 4-digit numbers that ...

Find the member of 4-digit numbers that can be formed using the digits 2,3,5,6,8 (without repetition). How many of them are
divisible by 3

Text Solution

Verified by Experts

The number of 4-digit numbers that can be formed using the 5 digits 2,3,5,6,8 is `""^(5)P_(4)=120`
Divisible by 3: A number is divisible by 3 if the sum of the digits in it is a multiple of 3. Since the sum of the given 5 digits is 24, we have to leave either 3 or 6 and use the digits 2,5,6,8 or 2,3,5,8. In each case, we can permute them in 4! ways. Thus the number of 4-digit numbers divisible by 3 is
`2xx4!=48`.
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Knowledge Check

  • The sum of all 4-digit numbers that can be formed using the digits 2,3,4,5,6 without repetition is

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    B
    532280
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    D
    532380

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