How many numbers between 000 and 999 (like a bike lock) contain the digit 9 at least once?
Total numbers = 1000
Total numbers which don't have digit 9 = 9 * 9 * 9 = 729
Total numbers with at least one digit 9 = 1000 - 729 = 271 (ans)
How many numbers between 000 and 999 (like a bike lock) contain the digit 9 at...
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.
How many whole numbers less than 10,000 contain the digit 5?
how many integers from 0 through 999,999 contain the digit 4 exactly twice? how many integers from 1 through 1000000 contain the digits 6 at least once
How many five digit numbers contain no repeated digits, have no even digits, and the sum of their digits is 25?
(c) (5 points) How many even 5-digit numbers are there for which no digit is 0, and the digit 6 appears exactly once? For instance, 55634 and 16118 are such numbers, but not 63304 (has a 0), nor 63364 (too many 67s), nor 55637 (not even).
(1) (a) How many distinct 5-digit numbers (i.e. numbers between 20000 and 50000) cul be forni(XI using lhe digits { I, %, 3, 4, 5, 6 such lhat no digils repcai'. (Hint: Count all the distinct numbers with no restriction on the leading (most significant) digit and then subtract the count of numbers with restrictions on the 1st digit) (b) (i) How many arrangements are there of the letters of MATCH (i) Of these, how many have the letters M...
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 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.
4. (3 pts) A combination lock has a four-digit combination nin^ngn4, where ni,n2, ng, and n4 are integers in {0,1,...,9}. (a) (1 pt) How many lock combinations are possible if each digit can be repeated? (b) (2 pts) If the digits in the combination cannot be repeated, then what is the probability of someone guessing the correct four-digit combination? 3 4. (3 pts) A combination lock has a four-digit combination nin^ngn4, where ni,n2, ng, and n4 are integers in {0,1,...,9}....
Let S be the set of all 7-digit numbers which do not contain 0 in any place — that is, each element of S is a string of 7 digits with each digit chosen from the set {1, 2, 3, 4, 5, 6, 7, 8, 9}. How many elements of S are there that don’t contain the substring 123? To qualify as having 123 as a substring, the numbers 1, 2 and 3 must appear in order and consecutively. For...