Prove the handshake theorem. If n people all shake hands with each other, the total number of distinct handshakes is [n(n-1)]/2

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: how many integers from 1 to 1000 are multiples of 3 or 5 (or both)

A: We want to find number of integer from 1 to 1000 are multiples of 3 or 5 (or both)

Q: For what values of nn will the number of ways of selecting nn items from 60 exceed the number of…

A:

Q: Let N=34 * 34* 63* 270. What is the ratio of the sum of the odd divisors of N to the sum of the even…

A: The number N is calculated by the prime…

Q: Evaluate the sum 5+10+20+40+80+...+320, and enter its numerical value.

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Q: calculate 1+3+5+...+(2n-1) for n = 1,2...,6.

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Q: Using the digits 2 through 8, find the number of different 5-digit numbers such that: (a) Digits…

A: Hi thankyou for posting this question,  since you have posted multiple subparts  as per our policy…

Q: case. What is the relationship between the three numbers below? Explain why it is the xyzb xyz0b…

A: We will first write the given numbers in base 10 representation using the concept of radix…

Q: Consider sum 1+5+9+13+...+81 what is a6

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Q: Discrete Mathematics How many n-digit numbers are there with at least one of the digits 1 or 2 or 3…

A: when 1 is absent,  There are 8 digits at first i.e. 2,3,4,...,9. So upto n, there are (n-2) digits.…

Q: How many different five-digit numbers can be formed from the digits 1, 2, 3, 4, 5 where: No…

A: Here we have to find no of ways to find different five digit numbers.

Q: The kitchen, dining room, and living room of a house will be painted, each with a different color.…

A: Given that, Total number of colors =7 Total number of rooms =3 (Kitchen, dining room, living room)

Q: "find A2, A−2, and A−k (where k is any integer) by inspection."

A: NOTE: Refresh your page if you can't see any equations. . use the diagonal matrix formula

Q: Question the iff {an} one {bn3 are juro sequences Such that an = (x)2h + (yjzh and bn= (x)2th -(y)zh…

A: Introduction:       A grouping of numbers in a specific order is known as a sequence. On the other…

Q: . n > 5 only if n > 7.

A: Given that n>5 only if n>7

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

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Q: A baseball pitcher threw 3848 pitches during part of a recent season. Of these, 1372 were thrown…

A: a) The given information is, Number of strikes Number of throws 0 1,372 1 961…

Q: For which values of n does n! have n or fewer digits

A: Solution is as follows

Q: - Find every positive integer n with the property that 2" - 1 is divisible by n.

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Q: (6) Find the sum of the integers for 7 to 508 Tmelusive,

A: first term (a0) = 7last term( an) = 508,     d = 1 ( natural no.)first we have to find total no of…

Q: If n is 0 what is 8n

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Q: How did they find n?

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Q: Find the sum 3 + 8 + 13 + 18 + 23 + 28 + ... + 303

A: See that 3, 8, 13, 18, 23, 28, ... , 303 forms an arithmetic progression (AP) with the first term…

Q: Find the sum of all natural numbers n such that 2021-n/99 is a natural number ?

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Q: Mrs. Hill asked her students to express the sum 1+ 3+ 5+ 7+9+...+ 39 using sigma notation. Four…

A: Since , the given sum is 1+3+5+7...+39 So its a alternate odd numbers sequence with end number is…

Q: Discrete Mathematics: Prove that every prime number greater than 3 is either one or more or one less…

A: We need to prove that any prime number which is greater than 3 is either 1 more than or 1 less than…