such a way that all men are next together and all women are next together? (a) How many ways are there to pick 7 objects out of a set of 25 objects? (b) How many bitstrings of length 25 have exactly 7 1s?

Q: How many strings of length two can be formed by using the letters A, B, C, D E and F without…

A: Given letters, A, B, C, D, E, F We have to find number of strings of length two

Q: How many possible ways are there to arrange the six items into the four boxes in such a manner that…

A:

Q: In how many ways can one put 8 adults and 4 children in a row, such that no two children are next to…

A: We have given that there are 8 adults and 4 children in a row. Here our claim to to show in how many…

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: How many different passwords are possible? If a cell phone’s password consists of eight characters,…

A: Given that cell phone's password consists of eight characters. first character is 6. The number of…

Q: (a) How many three digit numbers can be formed from the digits 0, 1, 2, 3, 4, 5, 6 and 7 such that…

A: Any number which has 0 or 5 in the unit place is divisible by 5.  Case 1: when unit digit is 0 The…

Q: A computer system uses passwords that have six characters, and each character is one of the 26…

A: It is given that the first character has to be a Letter Digits : 0,1,2,3,4,5,6,7,8,9 : 10…

Q: the character

A: There are total 4 characters A,B,C,D and D is used exactly twice. Therefore , the combination for D…

Q: Let X and Y have the joint p. d. f. $2x for 0< x < 1; 0 < y < 1 otherwise f(x, y) = Then P (X + Y <…

A: Given  Information: Let X and Y are two random variables with joint pdf, fx=2x  , 0&lt;x&lt;1,…

Q: In how many ways can the letters of the word 'RETAIL' be arranged in such a way that the vowels…

A: The objective is to find out in how many possible ways can the letters of the word 'RETAIL' be…

Q: Assume that there are 10 girls and 12 boys in the neighborhood club, and a team of 7 is to be…

A: Assume that there are 10 girls and 12 boys in the neighborhood club, and a team of 7 is to be…

Q: Suppose the Department of Motor Vehicles uses six digits and the numbers 0 through 9 to create its…

A: Solution.

Q: How many different three digit numbers can be made from the set of integers {1,2,3,4,5,6,7,8,9} if…

A: The set of integers {1,2,3,4,5,6,7,8,9}

Q: How many three-digit numbers are possible under each condition? (a) The leading digit cannot be zero…

A: We know that 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 are digits in the number system.

Q: How many 6-digit numbers have three even and three odd digits? (The first digit cannot be zero.)

A: It is given that a 6-digit number is to be formed which will have three even and three odd digits.…

Q: In a group of people, 68 people can speak English, 45 people can speak in Arabic and 19 people can…

A: It is given that 68 people can speak English, 45 people can speak Arabic and 19 people can speak…

Q: How many 15 letter strings containing only a's, b's, and c's have 6 a's and 4 b's?

A: Given: 15 letter strings containing only a's, b's and c's

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: Suppose that a password is exactly six characters and each character is 1 of the 26 lowercase…

A: The number of lowercase letters is 26 and the number of integers is 10.

Q: How many four-digit numbers can be formed from the digits 0, 1, 2, 3, 4, 5 and 7 if each digit can…

A: i) Since we need a four-digit number, the first digit can never be zero. Thus, the number of ways to…

Q: Each character in a password of length six can be any uppercase letter from A-Z or any symbol from…

A:

Q: how many possible combinations are there for computer password that must contain six letters a…

A: Each of the places can take any letters from A to Z , as no repeat condition is given. Therefore,…

Q: Prove a number is divisible by 3 if and only if the sum of its digits is divisible by 3.

A:

Q: How many five​-digit numbers can be formed with the first two digits odd and the last three digits…

A: The number of digits need to be formed is five. The first two digits are odd and the last three…

Q: A license plate consists of   five symbols on each​ plate, where the first two symbols are letters…

A: Fundamental principle of counting : If an event occur in m ways an corresponding to it another event…

Q: How many ways to arrange 7 books on the shelf exist if two definite books are not placed together?

A:

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

A:

Q: How many ways are there to select a three character password in such a way that the first two…

A: How many ways are there to select a three character password in such a way thatthe first two…

Q: How many ways are there to construct a string of 4 digits if numbers cannot be repeated? Asume each…

A: The objective of this question is to find out the number of ways to construct a string of 4 digits…

Q: Suppose you have 30 books (15 novels, 10 history books, and 5 math books). Assume that all 30 books…

A:

Q: How many six-digit even numbers more than 200,000 can be formed using all of the digits 1, 1, 2, 2,…

A: Step 1: Step 2: Step 3: Step 4:

Q: For some particular website, the password must start with one of the letters a b or c. Then there…

A: Introduction: As the English alphabet has 26 letters from A to Z, and there are 10 digits from 0…

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…