Explain why, in any set of 11 positive integers, some two integers must have the same I's digit.

Q: The set of all odd numbers between 100 and 110 that are a multiple of 3

A: We need to find the set of all odd numbers between 100 and 110 that are a multiple of 3.List of all…

Q: Select two positive integers a and b with 5 <  a  ≤  20  and 5  <  b ≤  20.

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Q: How many positive integers less than 10000 are there which contain at least one 7 or at least one 9…

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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: What is the converse of: an integer has divisors other than 1 and itself, if an integer is…

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Q: Find the number of ways a 5-digit positive integer can be made such that in each of them every digit…

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Q: Texas is starting a lottery game. Play- ers use a machine that randomly selects 7 distinct numbers…

A: To calculate the probability that Texas will lose money, we need to determine the expected value of…

Q: Prove that the sum of any five consecutive positive integers is always a multiple of five.

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Q: Prove that an odd number multiplied by an odd number is odd.

A: The objective is to prove that an odd number multiplied by an odd number is odd.

Q: Suppose that 75% of students attend lectures for a particular course and 20% of students fall the…

A: Conditional probability : Conditional probability is a measure  of the probability of an event…

Q: Show that if seven integers are selected from {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}, there must be…

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Q: Suppose that a password is exactly six characters and each character is 1 of the 26 lowercase…

A: The number of lowercase letters is 26 and the number of integers is 10.

Q: Find 1000 consecuticve composite integers. (Do not write them out).

A: To find :  The  1000 consecutive composite integers.      Formula Used :   The n consecutive…

Q: 2. Prove that the difference of an odd integer and an even integer is odd.

A: Prove that the difference of an odd integer and an even integer is odd

Q: find all possible three-digit numbers that are of the form 75_ and are divisible by both 3 and 2

A: Since the number is divisible by 2 and 3, it must be divisible by 6.

Q: what two consective odd integers have a product of 63?

A: Find two odd integers.