Discrete Math: Q# 1. How many strings of 9 letters can be created if the first and last letter must be the same? Is this 26^8 * 25?  Q#2. How many ways can a president, a vice-president, and a treasurer be chosen from a committee of 20 people? Is this 1140? I got this using the combinatorics definition using P(20,3)=20!/3!(20-3)1 Or is it 20!/(20-3)!=6840? I'm not sure which one to use. Q#3. How many numbers are there between 5 and 157 that are divisible by 3? Is this 52-3+1=50? I'm just going over some practice questions and want to make sure I'm on the right track. Thanks :)

Q: Suppose A = {2, 5, 7, 9, 13, 25, 26}. (a) Find n(A). n(A) =  (b) True or false: 7  A True False…

A: Given: A = {2, 5, 7, 9, 13, 25, 26}. The event A contains the outcomes 2, 5, 7, 9, 13, 25, 26.

Q: Find the number zeroes with which the decimal representation of 700! terminates. a (a) 245 O (b) 199…

A: The objective is to find the number of zeroes with which the decimal representation of 700!…

Q: Can you use mathematical induction to show that 4 divides 32x + 7 First define the predicate ?(x)

A: given , expression :- 32x+7 we have to prove that given expression is divisible by 4 .

Q: (a) Find the number of integers between 32 and 395 that are divisible by 6. (b) Find their sum.

A: (a) The first term of the integers between 32 and 395 is a1=36 which are divisible by 6   and the…

Q: show that n(n^2-1)(n+2) is divisible by 4 for all integers n

A: To show that n(n^2-1)(n+2) is divisible by 4 for all integers n

Q: 3. In this problem we use the notation for the digits a; of an integer m given by m = (akak-1...ao)…

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Q: 10. Find the sum of the coefficients of (2x– 3)°. c. -6560 d. -5120 а. -5660 b. -6780

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Q: >(6k – 4)(7k + 3) - k=1 Enter your answer as a number without any arithmetic symbols. Sum =

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Q: Can you help me explain why (k(k+1)) / 2 is an integers

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Q: Suppose that a and b are integers, c b = 3 (mod 19). Find the integer c that a) с%3D 13а (mod 19).…

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Q: (S+a?) (s*+b?)

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Q: Explain why it is convenient to write the expression for the number of possible permutations in…

A: It is efficient and time saving, imagine if you want to write 4! in its entire multiplication form…

Q: 3. Let n ≥ 9 be an integer. Give a combinatorial proof of the identity n-5 k n - () = (^=) ("=^). 9…

A: Here n>=9 (Given )  n belongs to N There are 'n number of balls and We have to choose 9 ball from…

Q: 21,−9,−39,−69,… Write the recursive rule

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Q: Suppose L = {+, x, S, <, 0} is the first-order language of number theory (Peano's arithmetic). Write…

A: Given that L=+,×,S,&lt;,0 is the first order language of number theory (Peano's arithmetic). Now we…

Q: Use different ways to show all possible combinations in this situation

A: Here given ,  there are three brand for cell phone  and there are 3 color for cell phone

Q: 4. Let (bn) be a sequence defined by 4bn-2 - bn-1 n > 2 b, n = 1 -1 n = 0

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Q: e the recursive formul

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Q: Show that 42n -1 is divisible by 5 for n>0

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Q: Number 332 – 1 has exactly two divisors greater than 75 and less than 85. What is their product?

A: We need to find two divisors of 332-1 between 75 and 85.  Now, we can use the identity a2-b2=a-ba+b…

Q: |(62" + 52") de Find + C

A: To find ∫6x4+5x5dx

Q: Evaluate        5  -2 [ ∑ (n-2)2 ]      n=1

A: We know  ∑i=1n xi = x1+x2+ ⋯ + xn