How many eight-digit positive integers have the sum of digits being even?

Expert Solution

Colby Messinger answered 2 years ago

How many different positive integers less than 1000 have distinct digits and are even? My attempt:...

How many different positive integers less than 1000 have distinct digits and are even? My attempt: since 1 digit numbers have the repeating 0 digit i started with 2 digit numbers. xxx= First digit: can only be 0 Second digit: can be any of 9 digits Third digit: can't be 0 or the digit used in the tens column so one of 4 numbers. 1*9*4= 36 ways so 1 * 9 * 4= 36 ways Now for the 3 digit...

1. A) How many three-digit numbers are there for which the sum of the digits is...

1. A) How many three-digit numbers are there for which the sum of the digits is at least 25? B) How many three-digit numbers can be formed if only odd numbers are allowed to be re-used Please combinatorics principles where applicable.

How many positive integers less than 1,000,000 have exactly one digit that is 7 and the...

How many positive integers less than 1,000,000 have exactly one digit that is 7 and the product of this digit (7) with the sum of other digits is between 50 and 65?

1. How many 6 digit strings have a sum of 35? in a digit string the...

1. How many 6 digit strings have a sum of 35? in a digit string the first digit can be zero 2. In how many ways can one arrange the set {A,B,C,D,E} if E can not be on either end of the string A must be in an even position B must be in an odd position (Solve by direct method and P.I.E.)

Question: How many even four-digit numbers can be formed from the digits 0,1,2,5,6 and 9. If...

Question: How many even four-digit numbers can be formed from the digits 0,1,2,5,6 and 9. If each digit can be used exactly once. Note: Using the rule of multiplication, solve the question elaborating and explaining each step in detail for my better understanding.

How many base 10 numbers have five digits? How many five digit numbers have no two...

How many base 10 numbers have five digits? How many five digit numbers have no two consecutive digits equal? How many have at least one pair of consecutive digits equal?

%) Even integers with non repeating digits. Even integers are integers ending in 0, 2, 4,...

%) Even integers with non repeating digits. Even integers are integers ending in 0, 2, 4, 6, 8. It is easy to see that for 2 digits integers, the number of 2 digits even integers is 45 (i.e. from 10 to 99, 10, 12, 14, …, 96, 98 are the 2 digits even integers); for 3 digits integers, the number of 3 digits even integers is 450 (from 100 to 999, 100, 102, 104, .. , till 994, 996, 998),...

How many even 4-digit numbers can be formed from the digits 1, 2, 3, 6, and...

How many even 4-digit numbers can be formed from the digits 1, 2, 3, 6, and 9 with no repetitions allowed? (Hint: Try filling the units place first.)

Determine a two digit number whose value is equal to eight times the sum of its digits and when 45 is subracted from the number, the digits are reversed?

How many 7-digit telephone numbers are possible if the first digit cannot be eight and (a)...

How many 7-digit telephone numbers are possible if the first digit cannot be eight and (a) only even digits may be used? (b) the number must be a multiple of 10 (that is, it must end in 0)? (c) the number must be a multiple of 1,000? (d) the first 2 digits are 92? (e) no repetitions are allowed?

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