(8) How many integers in the set [1,000] = {1, 2, ..., 1,000} are (a) divisible by 5? divisible by 3? (b) divisible by 5 and divisible by 3? (c) divisible by 5 or by 3? (d) divisible by neither 3 nor 5? (e) divisible by exactly one of the numbers 3 or 5?

Q: How many integers from 1 to 700 (inclusive) are divisible by the factors of 70 greater than 1?

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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: Use the roster method to write the set of integers between 0 and 12

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Q: 3. Consider a set of numbers B = {n E Z|1<n< 900} Answer the following questions. (a) How many…

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Q: How many seven-digit numbers can be formed with the first two digits odd and the last five digits…

A: The total number of digits from 0 to 9 is 10.

Q: (a) How many three digit numbers can be formed from the digits 0, 1, 2, 3, 4, 5, 6 and 7 such that…

A: Any number which has 0 or 5 in the unit place is divisible by 5.  Case 1: when unit digit is 0 The…

Q: Any whole number is divisible by 3 if and only if the sum of its digits is divisible by 3 TRUE FALSE

A: We have to state that the given statement is true or false.   Any whole number is divisible by 3 if…

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 integers in {1, 2,..., 100} are not divisible by 7 or 5? (Give the exact number)

A: Find the number of integers in 1,2,...,100 which are not divisible by 7 or 5.

Q: In a group of people, 68 people can speak English, 45 people can speak in Arabic and 19 people can…

A: It is given that 68 people can speak English, 45 people can speak Arabic and 19 people can speak…

Q: Find the number of positive integers not exceeding 104 that are not divisible by 5 or by 7.

A: In this Question we have to find the number of positive Integer between 0 and 104 which is not…

Q: How many positive integers less than 1000 are divisible by 5? How many positive integers less than…

A: We will answer the first three questions as per our guideline. Please resubmit the other question…

Q: How many positive integers less than 1000 (1) are divisible by 7? (2) are divisible by 7 but not by…

A: # As per the guidelines we are entitled to solve three subparts at a time, please resubmit the other…

Q: How many four-digit numbers can be formed from the digits 0, 1, 2, 3, 4, 5 and 7 if each digit can…

A: i) Since we need a four-digit number, the first digit can never be zero. Thus, the number of ways to…

Q: 3. (a) How many positive integers divide 10!. (b) How many partitions does the set [10] = {1, 2,…

A: Given, set={1,2,3,4,5,6,7,8,9,10} we have to calculate number of partitions required in which each…

Q: How many integers in {1,2, 3, ..., 99, 100} are not divisible by 7? (Give the exact number)

A: The given set of numbers is, 1,2,3,.....,99,100 The total no.of numbers from 1 to 100 is, 100 The…

Q: 7. Show that for every natural number n2 1, the integer ) + () +*(;) + - +) +22 +... +2" is…

A: Using binomial theorem:  n0+2n1+22n2....2nnn=n01n·20+n11n-1·21+n21n-2·22....nn1n-n·2n…

Q: How many integers between 1000 and 9999 inclusive are not divisible by 5?

A: The number of integers from 1 and 9999 which are divisible by 5 is = [9999 ÷ 5] = [1,999.8] = 1999…

Q: (a) Determine if the following numbers are prime: 101! + 78, 88! + 55 (b) Is 299 + 1 divisible by…

A: A prime number cannot be divided by any other number except 1 and itself. Now use this definition to…

Q: 3. Prove or disprove [yes, these should look familiar from §2.3]: (a) The sum of three consecutive…

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Q: 6. Where is 50 + 5 located on a number line? a) between 7 and 8 b) between 8 and 9 c) between 9 and…

A: 50=7.075=2.23

Q: (a) Suppose that there are k distinct positive integers that divide an odd positive integer n.…

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Q: [Q1] From the letters {A, B, C, D, E, F, G}, how many: (a) 3-distinct-letters co can be generated?…

A: Given: There are 7 letters A, B, C, D, E, F, G

Q: How many three digit numbers (values between 100 and 999 inclusive) are divisible by four? How many…

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