2. In how many ways can a fragger, a sniper and a medic be chosen from among 7 soldiers? 3. Suppose a landline number contains 5 digits. How many different landline numbers can be made with the digits 0-9 if no digit is used more than once and the first digit is not 0? 4. How many words can be formed with the letters of the word "IZOLA" with or without

Q: In how many ways can the letters of the word HORRAR be arranged if vowels are together?

A: Given information- We have given the letters of the word- HORRAR We have to find a number of ways to…

Q: 4. Suppose Pat has eight shirts and four pairs of pants. How many different outfits can Pat make by…

A: Every shirt combines with every pair of pants to make an outfit.  Shirt 1 creates an unique outfit…

Q: 2. In how many ways can 9 persons be seated in a round table with 9 chairs? 3. In how many ways can…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 23. How many even three digit numbers greater than 400 can be formed from 1, 2, 3, 4, 5, 6, 7, 8,…

A: Given that, 23. How many even three digit numbers greater than 400 can be formed from 1, 2, 3, 4, 5,…

Q: 4. How many five-letter codes can be formed from the letters of the English alphabet if repetitions…

A: Solution: Number of English alphabet  letters = n= 26

Q: 1. In how many ways can 2 red beads, 3 blue beads, 2 yellow beads, and white beads be arranged in a…

A: Ans#1- In how many ways can 2 red beads, 3 blue beads, 2 yellow beads, and white beads…

Q: In how many ways can 6 boys and 6 girls be seated around a circular table if all the no girls are…

A:

Q: In how many different ways can 5 bicycles be parked if there are 7 available parking spaces?

A: There are 7 available parking spaces and 5 bicycles.

Q: In how many ways can 7 graduate students be assigned to 1 triple and 2 double hotel rooms during a…

A: We can interpret this question as how to split seven students into groups of 3, 2 and 2.

Q: What if the jelly bean machine gives 3 jelly beans to the first customer who put in a coin, 4 to the…

A:

Q: There are 10 students in a class. In how many ways can an instructor give at most three students a…

A: n = 10 Let x represent the number of students given grade A.   The number of ways a student can be…

Q: How many different 7-letter words can be made a. if the first letter must be G, X, P, or L and no…

A: Concept: Since, in every case first letter shoud be G, X, P, or L.  Hence, total number of ways for…

Q: 6. In how many ways be 5 couples be seated in a round table if each couple consists of a man and a…

A: 6) Given that,  There are 5 couples and they are to be seated in a round table such that each couple…

Q: From a list of 40 teachers, 5 are to be promoted to subject area coordinator. In how many ways can…

A: Given: n=40 and r=5.

Q: IV How many different number plates for cars could be made if each number plate contains four (4) of…

A: Hi! Thank you for the question As per the honor code, We’ll answer the first question since the…

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: 1. He will repair 2 broken cars in a week 2. Out of 26 pending cars, he will fix more than 50% in a…

A:

Q: How many three-letter "words" can be made from 7 letters "FGHIJKL" if repetition of letters (a) is…

A: It is given that there are 7 letters available in “FGHIJKL”.   a). Since, the repetition of letters…

Q: How many different 7-letter words can be made a. if the first letter must be E, X, T, or L and no…

A: Permutation: A permutation of a set is defined as an arrangement of its members into a sequence or…

Q: 1. How many different license plates are possible using 3 letters followed by 3 digits? digits and…

A:

Q: 1. There are 3 similar Mathematics books, 2 similar Science books, 4 similar Filipino books, and 3…

A: We are entitled to solve only 1 question at a time so I am providing the same. Kindly repost the…

Q: How many three-letter "words" can be made from 10 letters "FGHIJKLMNO" if repetition of letters (a)…

A: Solution: 39. From the given information, the 10 letters are “FGHIJKLMNO”.

Q: In how many ways can 9 books be arranged on a shelf if 5 particular books must always stand…

A:

Q: (1). How many different words (including nonsense words) can you make by rearranging the letters of…

A: 1) The given word is “EFFERVESCENCE”. The total number of letters is 13. There are 2 C’s, 5 E’s,…

Q: In how many ways can 3 student, 4 teachers and 4 workers sit in a line if the teachers always set…

A:

Q: The new license plates consists of three alphabet letters followed by three digits.  How many…

A: Given: A license plate consists of three alphabet followed by three digits. The objective is to…

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

A:

Q: In how many ways can you make any arrangement of 3 vowels and 5 consonants taken from the alphabet…

A: In how many ways can you make any arrangement of 3 vowels and 5 consonants taken from the alphabet…

Q: 41 children need to be assigned to five Tee ball teams. The league wants each team to have 8…

A: Given that, 41 children need to be assigned to five Tee-ball teams. In order to assign all the…

Q: How many different 6-letter words can be made a. if the first letter must be B, Y, P, or M and no…

A:

Q: 5. From the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9, if six-digit numbers are to be formed and…

A: 5) Total number of digits to be used 8 Unit digit can hold any of the 4-digits; 3,5,7,or 9 for an…

Q: If repetitions are not permitted, from the 6 digits 0, 2, 3, 4, 5, and 8, how many 4- digit number…

A:

Q: In how many ways can the first 5 consonants be paired with the vowels of the English alphabet?

A: There are 5 vowels in English alphabets. So 1 consonant can be paired with 5 vowels in 5 ways.…

Q: 23. How many ways may 5 students be elected from a club with 45 members? 24.How many two-digit…

A: 23) Total number of members = 45 Number of members to be selected = 5 Number of ways the selection…

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: 2. In how many ways can 3 men and 4 women be seated on a bench if the women must be seated together?

A: Note: Since you have asked multiple question, we will solve the first question for you. If youwant…

Q: 5a. In a club consisting of 15 members, how many different ways can a 4-person committee where…

A: Determine the number of ways that a 4-person committee where everyone is considered equal. The…

Q: How many 4-digit numbers can be formed from the digits 0,1,2,3,4,5,6,7 and 8, if each digit can be…

A:

Q: 3. How many different 5-digit identification tags can be made a.if the digits can be used more than…

A: Given: Number of digits in an identification code = 5 Total number of digits = 0 to  9 = 10

Q: 2. How many 4 letter arrangements can be made from the letters MILKE D?

A: Explained below

Q: 3. Suppose a landline number contains 5 digits. How many different landline numbers can be made with…

A: As per Bartleby guideline expert have to answer first question only..

Q: 2. In how many ways can the 7 Harry Potter books be arranged shelf? on a

A: The objective is to find the number of ways to arrange 7 Harry Potter books on the shelf.

Q: How many three-letter "words" can be made from 10 letters "FGHIJKLMNO" if repetition of letters (a)…

A: Without Repetition : The number of ways to draw a 'r' units from 'N' population of units by using…

Q: requires eight letters for user names. lower and upper-case letters are considered the same. how…

A: It is an important part of statistics. It is widely used.

Q: 3. In how many different ways can the letters of the word 'OPTICAL' be arranged so that the vowels…

A: The word OPTICAL has three vowels O,I and A. Consider these three letters as 1 and the remaining…

Q: How many words, with or without meaning, each of 3 vowels and 3 consonants can be formed from the…

A:

Q: In how many ways can a teacher arrange 6 students in the front row of a classroom with a total of 20…

A:

Q: In how many ways can 3 students be selected from a group of 12 students to represent a university in…

A: Given data: Total students = 12 3 students  selected  randomly To find: In how many ways can 3…

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.