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 arrangements are there of the letters of the word MATHEMATICS in which all the vowels…

A:

Q: How many outfits can be made from 4 pairs of slacks, 5 shirts, and 3 ties, if one selection from…

A: First decide on a pair of slacks.For that there are 4 different choices.Now for each of those…

Q: How many different passwords of 4 characters can be made using the numbers from 0 to 9 and the…

A: A password of four characters is to be made using the numbers from 0 to 9 i.e. 10 digits and the…

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: 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: How many 6-places license plates are possible if he first 3 places re to be occupied by letters and…

A: Given data: How many 6-places license plates are possible if he first 3 places are to be occupied by…

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: 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: How many 3-digit numbers can be formed from the digits 2, 3, 5, 6, and 9, which are divisible by 5,…

A: Given information- We have given the digits- 2, 3, 5, 6, and 9. We have to form the 3 digits numbers…

Q: In how many ways can the numbers from 7 to 10 be arranged three at a time if the numbers can repeat?

A: If we have n numbers and we want to arrange k of them where the numbers can repeat, then the total…

Q: Assume that you select digits from the set {1,2,3,4,5,7,8} to form a number between 10 and 800. (1)…

A: given set of digits is  {1,2,3,4,5,7,8}  and the range of numbers is 10 to 800. There would be 2…

Q: How many ways to arrange 5 books on the shelf exist if two definite books are not placed together.

A:

Q: How many permutations of the numbers (1, 2, 3, 4, 5, 6, 7, 8, 9} have the numbers 4, 5 and 6 in…

A: So, the numbers 4, 5 & 6 should remain at their natural position and the other numbers can…

Q: How many 5–digit (decimal) integers are there with none of the digits repeated?

A:

Q: (b) How many three digit numbers can be formed from the digits 0, 1, 2, 3, 4, 5, 6, 7 and 8 such…

A: Given Digits: 0,1,2,3,4,5,6,7 & 8

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: Assume that you select digits from the set {2,3,5,7} to form a number between 20 and 700. (1) How…

A: The given set of digits is 2,3,5,7 and the range of numbers is 20 to 700. There would be 2 digit…

Q: How many numbers between 1 and 10000 have the digits 1,3, and 5 such that each digit appears exactly…

A: Here Numbers between 1 and 10,000 have digits 1,3,5 and each appears exactly once only

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: How many ways can all the etters in the word EDUCATION can be arranged if all the vowels are right…

A: The word education has 9 letters in which 'AEIOU69f4fc43-162e-4e8b-82a6-efea9c821b47' are vowels.…

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

A:

Q: 3n couples and their one child sit at a round table in such a way that their one child is between a…

A: It is given that there are 3n couples and their one child sit at a round table in such a way that…

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 4 digit numbers can be formed using only the numbers 3 2 7 6 0 4 9 if the number is odd and…

A: numbers: {3,2,7,6,0,4,9} make 4 digit numbers  no repeatation odd numbers: last digit must be odd.…

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 distinct four-digit integers can one make from the digits 1,3,3,7,7, and 8?

A: How many distinct four-digit integers can one make from the digits 1,3,3,7,7, and 8?

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: how many 3-digit number we can form using 10 digits (0,1,2,3.......,8) if no repetition is allowed

A: The first digit have 9 choices (digits 1 -9) as zero cannot be the first digit.There will be 9…