how many three digits multiple of 3 can be written using number 1,3,5,9 if all digits are difference
Answers
A three digit number is to be formed from given 9 digits 1,2,3,4,5,6,7,8,9.
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HTO
⇒Now, there are 9 ways to fill Ones place.
⇒Since repetition is not allowed, so Tens place can be filled by the remaining 8 digits.
So, tens place can be filled in 8 ways.
⇒Similarly, to fill Hundreds of places, we have 7 digits remaining.
So, hundreds can be filled by 7 ways.
⇒So, the required number of ways in which three-digit numbers can be formed from the given digits is 9×8×7=504
The response is 12.
Given:
1,3,5,9 are the number.
To Locate:
1) The number 1,3,5,9 can be used to create three-digit multiples of three.
2) A sum of numbers must divide by three in order for it to be a multiple of three.
3) Thus, three-digit numbers that can be divided by three are as 1+3+5=9, which is divisible by 3, we get 135
4) 153 as 1+3+5=9 which is divisible by 3
5) 315 because 1+3+5=9 and 3 is a divisor of 9.
6) 351 since 1+3+5=9, which may be divided by 3,
7) 513 because 1+3+5=9 and 3 is a divisible number
8) 531 because 1+3+5=9 and 3 is a divisor
9) 159 as 1+5+9=15 which is divisible by 3
10) 195 is divisible by 3 since 1+5+9=15.
11) 519 since 1+5+9=15, which can be divided by 3,
12) 591 as 1+5+9=15 which is divisible by 3
13) As 1+5+9=15, which is divisible by 3, the number 915
14) 951 since 1+5+9=15, which can be divided by 3,
Therefore, there are 12 three-digit numbers which are multiples of 3.
Hence answer is 12.
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