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Q: How many six digit numbers are there in which no digit is repeated even digits appeared in the even places and odd digits in the odd places and the number is divisible by 4?

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There are 5! = 120 such numbers.

No. 26 for instance the sum of the digits is 8 but not divisible by 4. 32 the sum of the digits is 5 but divisible by 4 The rules for some other numbers are 2 all even numbers are divisible by 2 3 The sum of the digits is divisible by 3 4 The last 2 numbers are divisible by 4 5 The number ends in a 0 or 5 6 The sum of the digits is divisible by 3 and is even 7 no easy method 8 The last 3 numbers are divisible by 8 9 The sum of the digits is divisible by 9

All numbers that are divisible by 6 are even numbers whose digits add up to 3 or a multiple of 3. Example : 284 is not wholly divisible by 6 as although it is even, its digits total 2 + 8 + 4 = 14 which is not divisible by 3. 282 is divisible by 6 as it is even and its digits total 12 which is divisible by 3.

The sum of the digits in odd position minus the sum of the digits in even position is divisible by 11.

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There are 5! = 120 such numbers.

1038, for example.

192 ways

98,764

If the digits may not be repeated, there are 6x5x4x3x2x1 = 720 numbers, If digits can be repeated, the answer is 6x6x6x6x6x6 = 46,656 numbers If zero is ong the available digits but is excluded from the first place. 5x6x6x6x6x6=38,880 numbers

No. 26 for instance the sum of the digits is 8 but not divisible by 4. 32 the sum of the digits is 5 but divisible by 4 The rules for some other numbers are 2 all even numbers are divisible by 2 3 The sum of the digits is divisible by 3 4 The last 2 numbers are divisible by 4 5 The number ends in a 0 or 5 6 The sum of the digits is divisible by 3 and is even 7 no easy method 8 The last 3 numbers are divisible by 8 9 The sum of the digits is divisible by 9

numbers that are divisible by 4 is either: 4n or numbers in which the number formed by last two digits are divisible by 4

All numbers that are divisible by 6 are even numbers whose digits add up to 3 or a multiple of 3. Example : 284 is not wholly divisible by 6 as although it is even, its digits total 2 + 8 + 4 = 14 which is not divisible by 3. 282 is divisible by 6 as it is even and its digits total 12 which is divisible by 3.

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All whole numbers are divisible by 1. Numbers are divisible by 2 if they end in 2, 4, 6, 8 or 0. Numbers are divisible by 3 if the sum of their digits is divisible by 3. Numbers are divisible by 4 if the last two digits of the number are divisible by 4. Numbers are divisible by 5 if the last digit of the number is either 5 or 0. Numbers are divisible by 6 if they are divisible by 2 and 3. Numbers are divisible by 9 if the sum of their digits is equal to 9 or a multiple of 9. Numbers are divisible by 10 if the last digit of the number is 0.

757

It is possible to create a 3-digit number, without repeated digits so the probability is 1.

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