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How many four digit numbers consist of only even digits?
256 unless you count zero in which case its 625.
How many even two digit numbers are there where the sum of the digits is 5?
To find the even two-digit numbers where the sum of the digits is 5, we need to consider the possible combinations of digits. The digits that sum up to 5 are (1,4) and (2,3). For the numbers to be even, the units digit must be 4, so the possible numbers are 14 and 34. Therefore, there are 2 even two-digit numbers where the sum of the digits is 5.
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?
There are 5760 such numbers.
What fraction of all 4 digits natural numbers have a product of their digits that is even?
To find the fraction of 4-digit natural numbers with a product of their digits that is even, we first need to determine the total number of 4-digit natural numbers. There are 9000 such numbers (from 1000 to 9999). Next, we consider the conditions for the product of digits to be even. For a number to have an even product of digits, at least one of the digits must be even. There are 5 even digits (0, 2, 4, 6, 8) and 5 odd digits (1, 3, 5, 7, 9). Therefore, the fraction of 4-digit natural numbers with an even product of digits is 5/10 * 9/10 * 9/10 * 9/10 = 3645/9000 = 809/2000.
What is the rule for numbers divisible by 11?
The sum of the digits in odd position minus the sum of the digits in even position is divisible by 11.
