A DNA molecule is shown below. A nucleotide is represented by one of the letters (a, t, c, g}. A codon is defined to be a triplet of nucleotides. The order of the nucleotides in a codon is significant, and the nucleotides can be repeated. These codons are important in determining how DNA is transformed into protein. How many different codons are possible? codons

Q: The game Capture is played by two players, First and Second, who take turns to move towards one…

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Q: Find all possible replacements for w (where w is a number on the clock) to make 2w = 6 in the…

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Q: let A {a, b} and B = {4, 5, 6}. %3D

A: A=a,bB=4,5,6 To find : a A×Ab B×B

Q: runners are in a race. How many different ways can they finish in 1 , 2 st nd, and 3rd place?

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Q: How many three-letter permutations can be formed from the first nine letters of the alphabet?…

A: Given that  How many three-letter permutations can be formed from the first nine letters of the…

Q: How many permutations of the 32 letters can be made?

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Q: Use A−1 to decode the cryptogram.

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Q: Use A-¹ to decode the cryptogram. 1 22 79 -2 -1 6 8 34 75 -19 21 157 -1 10 38 0 13 43 -13 -1 57 0 13…

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Q: Generate the first six terms of the sequence defined by the recurrence relations. an= nan-1-an-2,…

A: The recurrence relation is, an=nan-1-an-2 The first 2 terms are -1 and 0

Q: How many arrangements have all 3 a's together?

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Q: How many distinct permutations can be made from the letters of the word MATHEMATICS?

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Q: Example 7.7 Find the (a) first, (b) second, (c) third and (d) fourth moments for the set of numbers…

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Q: 2 3 4 5 6 7 2 7 1 5 3 1

A: Here given permutation as 12345676271534

Q: a and b are positive integers, show that gcd(a,b) = gcd(a,a+b).  Discrete math questio

A: To prove that gcd(a, b) = gcd(a, a + b) for positive integers a and b, you can use the properties of…

Q: You want to arrange the letters of the word ”MISSISSIPPI” such that all the ’I’s come together. How…

A: MISSISSIPPI

Q: A bag contains four different balls colored Red, White, Blue, and Green. You cannot see into the bag…

A: If two balls are selected at random without replacement, For permutations, nPr = n!/(n-r)! Now, 2…

Q: *Pivd the general Seltion to the

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Q: How many permutations can be made out of the letters in the word CAROLINE taken 4 at a time?

A: There are 8 letters in the word CAROLINE. We can take 4 letters from 8 letters in 8P4=8!(8-4)!=1680…

Q: how many ways to choose 4 out of 10 candidates for the distict jobs

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Q: How many ways can exactly four of the radios be selected and donated to a local museum?

A: Someone owns 81 antique radios, all of which are distinct. Here we will use combination. nCr = n! /…

Q: The United States Senate has 2 senators from each of the 50 states. Select all methods that would…

A: First let us know about what is random sampling.  Random sampling is a sampling technique in which…

Q: In how many ways can we arrange the letters in the word T

A: Given word is "TOOTH". The letters are T, O, O, T, H. The number of letters is 5. And the letter "O"…

Q: .

A: Given

Q: 1 2 2 3 4 5 6 7 8 2 1 6 3 5 7 8 4 2 1

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Q: With U={1,2,3,..,9,10} and A={1,2,3,4,5} B={1,2,4,8}, C={1,2,3,5,7}, D={2,4,6,8}. Determine C' u D'…

A: Let X be the universal set and A be a subset of X. Then the complement of the set A is denoted as A'…

Q: Tennis balls are randomly toss into one of five trays. Determine the number of balls needed to…

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Q: Write each sigma notation in expanded form, or vice versa. Use m=1.

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Q: To sign-in an account, suppose 0' to 9' numbers and 'A' to 'Z' alphabets with upper case and lower…

A: Total no. of numbers=10 Total no. of alphabets=52 (26 Upper case and 26 lower cases) No. of…

Q: 13. Zoe wants to see if favorite genre of movie is associated with a person's gender. She collects…

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Q: (c) In how many different ways can you draw the cards such that they all have a different value?

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Q: Suppose the probability of winning a particular lottery is 1 in 14C7 • 7 or 24.024 If Juanita and…

A: The probability of winning the particular lottery is 1 in C714  or 124024.

Q: How many modified perfect faro shuffles are needed to return the cards to their original position in…

A: The farro shuffle is a method of shuffling playing cards, in which half of the deck is held in each…

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.