Consider the word DREAM. How many different ways the letters can be arranged? How many different ways the letters can be arranged if the word begins with A or E? How many different ways the letters can be arranged if the word does not begin with R?

Q: A committee of 6 U.S. senators is to be formed with 3 Democrats and 3 Republicans. In how many ways…

A: We have given that,  Number of Democratic senators = 69 Number of Republican senators = 31

Q: You need to create a new passcode for your iPhone, their are 10 numbers to choose from and your…

A: Remark: We know the number of different permutations of n distinct objects taken r at a time is nPr…

Q: A couple has narrowed down the choices of a name for their new baby to 4 first names and 6 middle…

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Q: How many 5 letter codes are possible from the first 7 letters of the alphabet? a.) letters can be…

A: Excel is used to obtain the line and bar graph for years of education and years of experience,…

Q: How many different ways can 2 letters from the word SELECT be arranged?   answer is 21 (b)…

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Q: It is desired to write a 3-digit number using the numbers 2, 3, 4, 5, 6. If each number is used only…

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Q: Of 10 possible books, you plan to take 4 with you on vacation. How many different collections of 4…

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Q: If 7 numbers will be used to form telephone numbers, how many possible telephone numbers can be…

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Q: In the local boating pond there are 11 plain wooden boats, each with a different number. The owner…

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Q: A license plate consists of 2 letters followed by 4 numbers, and to avoid confusion, the numbers 1…

A: GivenNo.of letters from A-Z =26No.of numbers from 1-0 excluding 1 and 0 = 8

Q: How many four letter words beginning and ending with a vowel without any letter repeated can be…

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Q: How many five-digit numbers can be formed from the digits 1, 2, 4,6,8,9& 0 if digit is repeated?

A: To make a 5 digit number 0 can not come at first. So for the first position there are 6 choices. And…

Q: How many ways can 4 baseball players and 3 basketball players be selected from 15 baseball players…

A: Total baseball players = 15 Total basketball players = 11

Q: A uniform store sells polo shirts for companies in 6 different colors, 3 types of materials, 2…

A: There are 6 different colors, 3 types of material, 2 sleeve sizes, and 12 sizes (6 for men, 6 for…

Q: In recent years, a state has issued license plates using a combination of two letters of the…

A: Given that, In recent years, a state has issued license plates using a combination of two letters of…

Q: six-digit numbers can be made using two 2's and two 3's?

A: Given that  We should made Six digit numbers Using two 2's and two 3's.   Since only two 2's and two…

Q: You can choose from seven science courses and five humanities courses. In how many ways can he…

A: Number of science course = 7 Number of Humanities course = 5 Total number of course = 7+5 = 12…

Q: Any possible arrangement of 8 letters is considered a word.  The letters are taken from 21…

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

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Q: There are 13 female board members and 17 male board members. How many ways are there to make a…

A: Given there are 13 female board members and 17 male board members. To find number of ways are there…

Q: How many 4-letter words can be made from the letters MATH if repetition of letters is allowed?…

A: Given: Letters M , A , T ,H  We need to find number of 4 letter words that can be made.

Q: a shelf holds 2 english books, 3 history books and 4 math books. In how many ways can you arrange…

A: Given : Number of English books = 2 Number of history books = 3 Number of Maths books = 4

Q: How many 4 digit numbers can be formed from the digits 0,1,2,3,4,5, and 6 if each digit can be used…

A: 1. we will first find how many 4 digits numbers can be formed. To formed 4 digit numbers from…

Q: How many license plates can be made using two letters followed by four digits (0-9), allowing…

A: From this given information, license plates can be made using two letters followed by four digits…

Q: How many three-letter "words" can be made from 8 letters "FGHIJKLM" if repetition of letters (a) is…

A: Permutation: It defines the number of possible ways an object can be arranged or ordered. The…

Q: There are 4 different Mathematics books and 5 different Science books. In how many ways can the…

A: Total number of ways that the books can be arranged is 5760

Q: In how many ways can you arranged 2 Math books, 3 Science books and 3 English books if only one book…

A: The total number of mathematics books are 2. The total number of science books are 3. The total…

Q: How many three-letter "words" can be made from 9 letters FGHIJKLMN'' if repetition of letters (a) is…

A: Permutation: It defines the number of possible ways an object can be arranged or ordered. The…

Q: How many three-digit number with no repeat can we make using digits from {1,2,3,4,5}

A: three-digit number with no repeat can we make using digits from {1,2,3,4,5} here we have 5 choices…

Q: How many arrangement of 8 letters taken from 5 vowels and 21 consonants can be made if there has to…

A: 21 consonants and 5 vowels. Given condition, 8 letter words using 5 consonants and 3 vowel.…

Q: How many six-digit numbers can be made using two 2's and two 3's? I always think that the other 2…

A: In the 6-digit number, there are two 2's, two 3's and the remaining two digits can be any from…

Q: Find the number of ways in which 5 economics books, 3 history books, and 2 mathematics books can be…

A: See the detailed solution below.

Q: 2. If a license plate consist of 3 letters followed by 3 digits, how many license plates are…

A: Here the repetition of letters and numbers are allowed.

Q: From 7 consonants and 5 vowels, how many words can be formed consisting of different consonants and…

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Q: A phone number in the United States consists of 10 digits, 3 for a area code and 7 for the phone…

A: Given Data: The number of digits whole phone number consists of: 10 digits The number of digits the…

Q: How many 3 digit numbers can be formed from the digits 2, 4, 6, 8 and 9 if repetitions are allowed?

A: Solution: From the given information, the digits are 2, 4, 6, 8 and 9.

Q: How many license plate containing two letter followed by three digit can be formed 2 If the letters…

A: License plate made up of 5 alphanumeric in which first two position taken by letters then last three…

Q: A committee of 6 U.S. senators is to be formed with 3 Democrats and 3 Republicans. In how many ways…

A: Combination Rule:A combination is a selection of all or part of a set of objects, without regard to…

Q: a football  tryout From a group of 15 people, a team  of 12 people is selected. In how many…

A: We havevto find no. Of combinations possible.

Q: In a certain country, the car number plate is formed by 4 digits from the digits 1, 2, 3, 4, 5, 6,…

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Q: How many passwords with 7 letters without repetition can be made from 15 letters

A: Given, Total no of letters n=15 Password length is r=7 number of different password of length 7…

Q: There are 4 different Mathematics books and 5 different Science books. In how many ways can the…

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Q: There are 9 female board members and 21 male board members. How many ways are there to make a…

A: given that there are 9 female board members and 21 male board members.

Q: A special plate number is made up of 2 letters of the vowel followed by 3 digit numbers. How many…

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Q: How many even three digits numbers can be formed from the digits 3,2,5,6 and 9if each digit can be…

A: We have to make three digit even number which means that last digit should be even number. Here,…

Q: Luiza has 10 different keys. In how many ways can she arrange the keys in a key chain?

A: luiza has 10 different keys .in how many ways can she arrange the keys in a key chain?

Q: How many ways are there to select an all-star team which includes all members from A, all members…

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Q: 2. In a certain country, license plate numbers have 3 letters followed by 3 digits. How many…

A: here use counting principle  for combination  nr = n!(n- r)! r!

Q: Sakura wants to create an identification code consisting of four letters followed by three digits.…

A: Given that code is to be made with 4 letters and 3 digits.

Q: Students were divided into 10 teams with 12 on each team. Later, the same day students were divided…

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