A DNA sequence can be represented as a string of the letters ACTG (short for adenine, cytosine, guanine, and thymine).   (a) How many DNA sequences are exactly 20 letters long?    (b) Given a DNA sequence of length 20, how many single letter mutations are possible?      (c) Given a DNA sequence of length 20, how many double letter mutations are possible?

Q: Suppose we want to choose 5 letters, without replacement, from 15 distinct letters. (a) How many…

A: Solution-: Here, n=15,r=5 We want to choose 5 letter, without replacement from 15 distinct letter.…

Q: In how many ways can you select two books to read from a shelf of ten books? (Order is important.)

A: Given thatr = 2 n = 10

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: Consider the following digits: 0, 1, 2, 3, 4, 5, and 6. if a three-digit number is to be formed and…

A:

Q: How many three-letter "words" can be made from 5 letters "FGHIJ" if repetition of letters (a) is…

A: Given5 letters is "FGHIJ"No.of letters = 5

Q: In Morse code, symbols are represented by variable-length sequences of dots and dashes. (For…

A: With a sequences of length 1 we can represent 2 symbols. With a sequence of length 2 we can…

Q: of 2 3. If you read 20 books this year, a. How many different sets of 6 books could you recommend…

A: Total number of books read this year, n = 20(a) To find the number of different sets of 6 books that…

Q: The average length of a password is 8 characters. If you are allowed to use the 26 letters in the…

A: The average length of a password = 8No. of letters in the alphabets=26No. of digits from 0-9=10Total…

Q: How many 4-digit odd numbers can be made from the digits 0; 2; 4; 5; 8; 9 if the number has no…

A:

Q: In one case a byte is defined as a sequence of 8 bits. Each bit can be either zero or one. How many…

A:

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

A: The word “jogging” contains a total of 7 letters in which “g” letter is repeated 3 times.

Q: In how many ways may Ana select 5 of her 10 friends to attend her birthday party? In how many ways…

A: Here use combination

Q: How many arrangements are there for the letters of the word "PIKACHU" with the CH together in the…

A:

Q: You are asked to create a six character password and each character can be any of the 26 letters of…

A: Given: Number of alphabets=26 Number of numerical 2 through 9=8 Total number of characters, n=34 The…

Q: A 16-bit string is a sequence of 16 symbols, each symbol a 0 or a 1. How many 16-bit strings are…

A: A bit string is a sequence of  symbols, each symbol a  or a We have to find the possible number of…

Q: In how many different ways can 9 people arrange themselves in a line to receive service from a…

A: Given information: There are total 9 people arrange themselves in a line to receive service from a…

Q: How many three-letter "words" (some may be nonsense words) can be made from 4 letters "FGHI" if…

A: Permutation and combination used to calculate the number of possible ways to arrange or select a…

Q: How many ways can you reorder the eggs in a carton of one dozen eggs? (Enter your answer as a whole…

A: We have to find this How many ways can you reorder the eggs in a carton of one dozen eggs.

Q: How many ways are there of arranging the 26 letters of the alphabet so that none of the words be,…

A:

Q: A computer user has downloaded 23 songs using an online file-sharing program and wants to create a…

A: GivenNo.of downloaded songs(n)=23no.of  songs to use in CD player(r)=8

Q: In how many ways is it possible to answer a 12-question true-false examination? The number of ways…

A:

Q: Many banks require customers who use the automated teller machine (ATM) to enter a four-digit…

A: ATM machine needs four digit password before transaction.  digits : {0,1,2,3,4,5,6,7,8,9} digits can…

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.