Given the digits {1, 2, 3, 4, 5}, how many 3-digit numbers can be formed if: No digit is repeated?  The result must be even, and no digit is repeated?  The number must contain at least 1 repeated digit?

Q: the set {1,3,4,6,7,8,9}, how many odd numbers can we construct between 100-999 if each element can…

A: We have to solve given problem:

Q: In a certain country, area codes have four digits and are subject to the following restrictions. The…

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Q: Suppose 35 cars start at a car race. In how many ways can the top 3 cars finish the race?

A: The information provided in the question are as follows :-There are  cars at a car race.

Q: if these five numbers form a pattern such that the differernce between each pair of numbers is the…

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Q: an iPhone locks with a 5-digit code. How many codes are possible, if repetition isnot allowed and…

A: Lock of 5 digit code , Repetition is not allowedFirst digit must be 9 Number of codes = ?

Q: How many multisets can we make using the integers 1 through n, if we require that no number appears…

A: It is given that the integers are from 1 through n, and no number appear more than 3 times.

Q: Prove: The sum of an odd number of odd numbers must be odd.

A: Let us prove this by induction, that if n is odd and a1,a2,. . .. .an are odd, then ∑i=1nai is odd.…

Q: Using the digits 0,1,2,....8,9 determine how many of each type of the three-digit number can be…

A: Given digits 0, 1, 2, ............., 8, 9 Any three digit number with zero at its first place…

Q: How many different two-digit numbers can you form using the digits 3, 8, 7, 4, 1, and 5 without…

A:

Q: c) List vertically all the ways each number 0-35 can be represented as a sum of two or more…

A: Assume that limiting the numbers to integers. Let's try a few and see if we can find a pattern:…

Q: How many ways can you have a 6-digit passcode on your phone if you start with a 9 and none of the…

A: We need to find the number of ways to have a 6-digit passcode, given that the first digit is 9 and…

Q: How many integers must you pick in order to be sure that at least two of them have the same…

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Q: To use an automated teller machine at a certain bank, you must enter a 4-digit code, using the…

A: Total available numbers = 9 To make 4 digit code

Q: How many hexadecimal numbers from 1 through FFFF do not have any repeated digits?

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Q: that if 3 divides the sum of the digits of n, then 3|n

A:

Q: Find the number of different 7-digit numbers which can be formed from the seven digits 4, 4, 7, 9,…

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Q: There are 12 black socks, 15 dark brown socks, and 20 dark blue socks in a drawer. It is dark and…

A: In a drawer, The number of Black Socks = 12 The number of Dark Brown Socks = 15 The number of Dark…

Q: How many different three-digit numbers can be formed using the digits 1, 4, 5, and 9 without…

A: Given N=4 n=3

Q: 20) Show that the sum of two consecutive integers is always odd.

A: Let x be any integer. Then its consecutive integer can be written as x+1.