Use mathematical induction to 3n(n+1) 3+6+9+12+...+3n=

Q: Evaluate the permutation. P(n,0) P(n,0) = (Simplify your answer.)

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Q: In certain state, license plates each consist of 3 letters followed by 3 numbers. (a) How many…

A: Since you have asked multiple subparts, we will solve the first three subpart questions for you. If…

Q: asubset of C

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Q: 7 identical prizes are distributed to a group of 21 people. How many ways are there to distribute…

A: The given details: 7 identical prizes are distributed to a group of 21 people. That is, Number of…

Q: selecting three (3) coins, but assume that there are 5 dimes, 4 nickels, and 2 quarters. In how…

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Q: A four digit number is to be formed from the digits 0, 2, 5, 7, 8. How many numbers can be formed if…

A: 4 ways to fill it (2,5,7,8) 5 ways to fill it (0,2,5,7,8) 5 ways to fill it (0,2,5,7,8) 5 ways to…

Q: How many ways you can draw 3 balls in a box of 5 balls, if we replace the ball in box after being…

A: Permutation: It means number of arrangements  be obtained  It is denoted by P(n,r) or Prn where n is…

Q: Suppose that an experimenter tossed three balanced coins. He defined X₁, to denote the number of…

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Q: Combination Locks A combination lock displays 50 numbers.To open it, you turn clockwise to the first…

A: Solution: Let the p selections for the first choice q selections for the second choice and  r…

Q: Proof by contradiction. There is no largest composite number

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Q: What is the difference between permutations and combination? Develop a mnemonic ( or something…

A: Permutation means arrangement of things or entities. The word arrangement is used, if the order of…

Q: (b) If P ú prime PXa and Pl ab. show that Pib using linear combination What ĥ c a; P) ?

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Q: The learners will illustrate the following numbers using the given representations ☆ 1 000 3360 5280…

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Q: A password for a computer system must have at least 8, but no more than 12, characters, where…

A: The password has lower case English letters , uppercase English letters a digit or one out of 6…

Q: showthat

A: The solution of the asked question is given as

Q: manual computation using F test

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Q: Polya's Problem in a basketball league consisting of 10 teams, each team plays each of the other…

A: For a match, 2 teams are to be selected. So, selecting 2 teams out of 10 teams :

Q: How many different ways can the letters of "kissing" be arranged? The number of different ways that…

A: We have given that a word ‘kissing’.

Q: 5 (K+1) K=1

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Q: How many subsets of S do not contain any upper case letters?

A: given set S=A,B,a,b,c,d,1,2,3,4 claim- to find how many subsets of Sdo not contain any upper case…

Q: How many ways are there to list the digits {1,2, 2, 3, 4, 5, 6} so that identical digits are not in…

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Q: 2 22 23 +... 2n 27

A: The result to be proved by mathematical induction is 12+122+123+......+12n=1-12n The sum of a G.P.…

Q: How many permutations are there? How many combinations are there?

A: Our aim is to find the  How many permutations are there? How many combinations are there?

Q: Proof the following

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Q: Using exponential generating functions, find the number of {0, 1, 2, 3, 4}-strings of length n with…

A: Given: Using the exponential generating function the objective is to find the number of {0,1,2,3,,4}…

Q: How many 3 digit numbers com we wing the digits 2,2,4,Ś cnd 6 withat bepelition? make

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Q: How many permutations of the letters PRODUCT have consonants in the second and third positions?

A: There are total 400 permutations of the letters PRODUCT have consonants in the second and third…

Q: Suppose ACB and BCC. Show that = {A, B-A, C-B} is a partition of C.

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Q: Delermine if the follo wing series Show diverges. Converpes or your

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Q: How many even 3-digit numbers can be formed from the digits 1, 2, 3, 6, and 9 with no repetitions…

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Q: Tossing a coin four times in a row and getting HTHT, in what order

A: we know that, when a tossing coin four times then , total outcomes= 2^4                         = 16

Q: A traveling agent has to visit four cities, each of them five times. In how many different ways can…

A: There are 205! 5! 5! 5!ways to visit 4 cities, each of them 5 times.

Q: what is the fuzzy power set ? And give examples

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Q: Define circular permutation. Write the formula to find the circular permutation of “X” different…

A: Permutation and combination are 2 methods in mathematics. Permutation deals with the number of ways…

Q: # Q.1 write an R script to receive 5 numeric input from keyboard vl<-

A: It is been asked to provide R code to receive 5 numeric input.