as there are 5 odd digits 1,3,5,7,9 with no repeated digits and sum is 25
number of ways to arrange them =5! =5*4*3*2*1 =120
therefore number of five digit numbers contain no repeated digits, have no even digits, and the sum of their digits is 25 =120
How many five digit numbers contain no repeated digits, have no even digits, and the sum...
13. For how many three digit numbers (100 to 999) is the sum of the digits even? (For example, 343 has an even sum of digits: 3+4+3 = 10 which is even.) Find the answer and explain why it is correct in at least two different ways.
Consider the number 35964 How many 3 digit numbers can be formed using digits from 35964 if no digits may be repeated? What is the sum on all of those 3 digit numbers?
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.
15. Given the digits 1, 2, 3, 4, and 5, find how many 4-digit numbers can be formed from them: (a) If no digit may be repeated. (b) If repetitions of a digit are allowed. (c) If the number must be even, without any repeated digit. (d) If the number must be even.
Show steps, answer is 13440 3. How many odd five-digit numbers have all the digits different? Explain how you arrived at your answer.
8. (6 points) How many six-digit numbers with a possible leading zero, but no repeated numbers are there if the digits 7 and 8 must appear in the number and must be next to each other?
How many 4-digit numbers can be formed using only the digits {1,2,3} if repetition is allowed and the number must contain the digit 3 somewhere. Hint: it may be easier to first count the numbers that don't contain the digit 3.
1. (a) (i) How many different six-digit natural numbers may be formed from the digits 2, 3, 4, 5, 7 and 9 if digits may not be repeated? (ii) How many of the numbers so formed are even? (iii) How many of the numbers formed are divisible by 3? (iv) How many of the numbers formed are less than 700,000? (b) JACK MURPHY’s seven character password consists of four let- ters chosen from the ten letters in his name (all...
Suppose that a "code" consists of 5 digits, none of which is repeated. (A digit is one of the 10 numbers 0,1 2,3 4,5 6,7 8,9.) How many codes are possible?
How many 6 digit numbers (in base 10) have all their digits in the set {8,9}? Please show work that leads to the answer.