1a. An ATM requires a four-digit PIN, using the digits 0-9. How many PINs have no...

1a. An ATM requires a four-digit PIN, using the digits 0-9. How many PINs have no repeated digits?

1b. How many ways can president and vice president be determined in a club with twelve members?

1c. A security team visits 12 offices each night. How many different ways can the team order its visits?

1d. In a certain lottery you select seven distinct numbers from 1 through 39, where order makes no difference. How many different ways can you make your selection?

1e. First, second, and third prizes are to be awarded to three different people. If there are ten eligible candidates, how many outcomes are possible?

1f. Three identical “Outstanding Teacher” awards are to awarded to three different people. If there are ten eligible candidates, how many outcomes are possible?

Expert Solution

Colby Messinger answered 1 year ago

1a) How many five digit number can be written with the digits 1,2,3,4 if there is...

1a) How many five digit number can be written with the digits 1,2,3,4 if there is an even number of twos? 1b) How many five digit number can be written with the digits 1,2,3,4 if two can be used either 4 times, or none?

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.

You need to create a four-digit password using 0-9. How many passwords are possible, without repeating...

You need to create a four-digit password using 0-9. How many passwords are possible, without repeating a number, if a password must not start with a 0?

How many valid 3 digit numbers can you make using the digits 0, 1, 2 and...

How many valid 3 digit numbers can you make using the digits 0, 1, 2 and 3 without repeating the digits? How about with repeating?

Consider four-digit numbers that consist of 0, 1, 2, 5, 6, and 9. a) How many...

Consider four-digit numbers that consist of 0, 1, 2, 5, 6, and 9. a) How many four-digit numbers can be formed from the digits 0, 1, 2, 5, 6, and 9 if each digit can be used only once? (the four-digit numbers can't start with 0). b) How many of those four-digit numbers are even? c) How many are greater than 2200?

Password consists of five characters: one lowercase letter and four digits 0 – 9. How many...

Password consists of five characters: one lowercase letter and four digits 0 – 9. How many possible combinations for the password are there if digits can be repeated? How many possible combinations for the password are there if digits can not be repeated? What is a percentage of passwords with repeated digits?

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?

From the digits 0,1,2,3,5,7,8, and 9 , selected of them at random and from a four-digit...

From the digits 0,1,2,3,5,7,8, and 9 , selected of them at random and from a four-digit number, none of these digits appears more than once in each number. (a) Find the probability that the number formed is even. (b) Find the probability that the number formed is divisible by 3.

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

In a four-digit lottery, each of the four digits is supposed to have the same probability...

In a four-digit lottery, each of the four digits is supposed to have the same probability of occurrence. The table shows the frequency of occurrence of each digit for 87 consecutive daily four-digit drawings. Digit Frequency 0 37 1 40 2 31 3 43 4 34 5 31 6 37 7 29 8 30 9 36 Total 348 (b) Calculate the chi-square test statistic, degrees of freedom, and the p-value. (Round your test statistic value to 2 decimal places and...

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