Count the number of 6-digit numbers with:
- Strictly ascending digits from left to right. For example 124579. Hint: any 6 distinct digits can be arranged in ascending order in a unique way.
- The answer is 84
- Ascending digits from left to right. For example 133588, 566666, 788888. (hint: choose 6 digits out of {1,2,⋯,9} with repetition).
What ascending means is that each number is at least the previous.
- Please solve the second part of the question.
Homework Answers
Part b)
If repeated digits are allowed such that each digit is at least the previous one (eg 133588), is n+r-1Cr
So,
n = 9 and r = 6 (6 digit no)
n+r-1Cr = 9+6-1C6 = 3003
Add Answer to:
Count the number of 6-digit numbers with:
Strictly ascending digits from left to right.
For example...
1. (a) (i) How many different six-digit natural numbers may be formed from the digits 2,...
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...
6. The digits 1,2,3,4 and 5 are randomly arranged to form a three-digit number. If digits...
6. The digits 1,2,3,4 and 5 are randomly arranged to form a three-digit number. If digits are not repeated, find the probability that the number is even and greater than 500? 7. A coin is tossed 10 times. Find the probability that at least one toss results in a tail. 8. A game is played using one die. If the die is rolled and shows 1,2 or 3, the player wins nothing. If the die shows 4 or 5, the...
Introduction: Ten digit ISBN numbers are created so that the first nine digits are information digits...
Introduction: Ten digit ISBN numbers are created so that the first nine digits are information digits and the last digit is a check digit. T his last number helps people notice and correct mistakes that might be made in recording the information digits. The same is true for thirteen digit ISBN numbers. Here is a ten digit ISBN number: 0-13-149498-8. The digit 0 indicates the book is written for English-speaking people. The number 13 and the number 149498 identify the...
[10 marks] Assume that we have two decimal positive numbers A and B. Both numbers have n digits. ...
[10 marks] Assume that we have two decimal positive numbers A and B. Both numbers have n digits. We want to know what is the minimum number of swaps that we need in order to get from number A to B, where in each swap we choose two digits of a number and simply swap them For simplicity, we assume that A and B do not have the digit 0 in them, and that A and B have the set...
Activity 5.4 What Are You Made of 30g Now, moving left to right, compare digits that have the sam...
Activity 5.4 What Are You Made of 30g Now, moving left to right, compare digits that have the same place value. The digit in the ones and tenths places is the same in bosh numbers. In the hundredths place, 8 is gremer than 5, and it follows that 2.682.657. Procedure Comparing Decimals 1. First compare the integer parts (to the left of the decimal point). The number with the larger integer part is the larger number 2. If the integer...
A large collection of one-digit random numbers should have about 50% odd and 50% even digits...
A large collection of one-digit random numbers should have about 50% odd and 50% even digits because five of the ten digits are odd (1, 3, 5, 7, and 9) and five are even (0, 2, 4, 6, and 8) a. Find the proportion of odd-numbered digits in the following lines from a random number table. Count carefully. 9 0 49 0 5 0 7 8 1 7 8 3 4 5 0 7 1 5 7 5 1 2...
BENFORD 25 POINTS (A) 5 POINTS Characterize all numbersエso that 1000 has leading digit 9. (B) 5 POINTS What is the leading digit of We pointed out before that there can be ambiguity in these sor...
BENFORD 25 POINTS (A) 5 POINTS Characterize all numbersエso that 1000 has leading digit 9. (B) 5 POINTS What is the leading digit of We pointed out before that there can be ambiguity in these sorts of expressions so think of this as the result of the following recursive definition of a sequence (B)where the above is just B (C) 15 POINTS Suppose we form random numbers in the following way Pick a random digit in 0,1,2,3,4,5,6,7,8,9) with each choice...
Banks issue credit cards with 16 digit numbers. If you've never thought about it before you...
Banks issue credit cards with 16 digit numbers. If you've never thought about it before you may not realize it, but there are specific rules for what those numbers can be. For example, the first few digits of the number tell you what kind of card it is - all Visa cards start with 4, MasterCard numbers start with 51 through 55, American Express starts with 34 or 37, etc. Automated systems can use this number to tell which company...
Credit card numbers follow certain patterns. A credit card number must have between 13 and 16...
Credit card numbers follow certain patterns. A credit card number must have between 13 and 16 digits. The number must start with the following: 4 for Visa cards 5 for MasterCard cards 37 for American Express cards 6 for Discover cards In 1954, Hans Luhn of IBM proposed an algorithm for validating credit card numbers. The algorithm is useful to determine whether a card number is entered correctly or is scanned correctly by a scanner. Almost all credit card numbers...
Problem 6. (20 points) Texting. You are competing with your friends to type text messages on your...
the pseudocode or precise description in words of the
algorithm
Problem 6. (20 points) Texting. You are competing with your friends to type text messages on your smartphone as quickly as possible. Here are the rules: you use two thumbs for texting and they start out on the bottom left and bottom right keys of the keyboard. To type a character, you move either thumb from its current key to the key you need to press, and it takes time...
6. The digits 1,2,3,4 and 5 are randomly arranged to form a three-digit number. If digits are not repeated, find the probability that the number is even and greater than 500? 7. A coin is tossed 10 times. Find the probability that at least one toss results in a tail. 8. A game is played using one die. If the die is rolled and shows 1,2 or 3, the player wins nothing. If the die shows 4 or 5, the...
[10 marks] Assume that we have two decimal positive numbers A and B. Both numbers have n digits. We want to know what is the minimum number of swaps that we need in order to get from number A to B, where in each swap we choose two digits of a number and simply swap them For simplicity, we assume that A and B do not have the digit 0 in them, and that A and B have the set...
Activity 5.4 What Are You Made of 30g Now, moving left to right, compare digits that have the same place value. The digit in the ones and tenths places is the same in bosh numbers. In the hundredths place, 8 is gremer than 5, and it follows that 2.682.657. Procedure Comparing Decimals 1. First compare the integer parts (to the left of the decimal point). The number with the larger integer part is the larger number 2. If the integer...
A large collection of one-digit random numbers should have about 50% odd and 50% even digits because five of the ten digits are odd (1, 3, 5, 7, and 9) and five are even (0, 2, 4, 6, and 8) a. Find the proportion of odd-numbered digits in the following lines from a random number table. Count carefully. 9 0 49 0 5 0 7 8 1 7 8 3 4 5 0 7 1 5 7 5 1 2...
BENFORD 25 POINTS (A) 5 POINTS Characterize all numbersエso that 1000 has leading digit 9. (B) 5 POINTS What is the leading digit of We pointed out before that there can be ambiguity in these sorts of expressions so think of this as the result of the following recursive definition of a sequence (B)where the above is just B (C) 15 POINTS Suppose we form random numbers in the following way Pick a random digit in 0,1,2,3,4,5,6,7,8,9) with each choice...
the pseudocode or precise description in words of the
algorithm
Problem 6. (20 points) Texting. You are competing with your friends to type text messages on your smartphone as quickly as possible. Here are the rules: you use two thumbs for texting and they start out on the bottom left and bottom right keys of the keyboard. To type a character, you move either thumb from its current key to the key you need to press, and it takes time...
Most questions answered within 3 hours.
-
find the critical value associated with a right sided hypothesis of
the mean using a sample...
asked 1 hour ago -
Which of the following statements is true with respect to a
simple linear regression model?
a....
asked 2 hours ago -
The energy required to remove an electron from a surface of a
solid element is called...
asked 3 hours ago -
How would you train your employees to avoid risks of using
mobile devices?
asked 3 hours ago -
Assume Kw = 1.01 ✕ 10−14
For pure water, we can calculate [H3O+ ] = [OH...
asked 4 hours ago -
Suppose that on a temperature scale X, water boils at 203.0°X
and freezes at -105.7°X. What...
asked 5 hours ago -
BaS crystallizes in a cubic unit cell with S2- ions on each
corner and each face....
asked 6 hours ago -
A. 0≤P(Oi)≤10≤P(Oi)≤1 for each i
B. P(Oi)≤0P(Oi)≤0
C. P(Oi)=1+P(OCi)P(Oi)=1+P(OiC)
D. P(Oi)≥1P(Oi)≥1
If an experiment consists of...
asked 7 hours ago -
A battery has an emf of 9.20V and an internal resistance of 1.20
ohm. a)What resistance...
asked 7 hours ago -
The area of an elastic circular loop decreases at a constant
rate, dA/dt = −6.60×10−3 m2/s...
asked 8 hours ago -
The denaturation of proteins can be described by the
equilibrium
F⇌U
where F and U represent...
asked 10 hours ago -
Please answer what the maximum and minimum force is, and the
angle on the ion is...
asked 10 hours ago