Suppose that in a particular Finite course, 5/14 of students plan on majoring in math, 11/42 plan on majoring in history, and 1/7 plan on double majoring in math and history. How many want to major in exactly one of history or math?

Q: In the 31st SEA Games volleyball match, how many ways can a coach choose 6 starters from a…

A: From given information, n is 15 and r is 6.

Q: Explain the difference between a permutation and a combination of n items taken r at a time.

A: Two types of counting problems occur so frequently that they deserve specialattention. These…

Q: How many permutations can be made out of the letters BOOKKEEPER?

A: From the given information, Number of letters in BOOKKEEPER = 10 There is 1 B, 2 O's, 2 K's, 3 E's,…

Q: In how many ways can we arrange 3 boys and 3 girls in a circular table if:  All boys and girls are…

A: Given, 3 boys and 3 girls       To find, In how many ways can we arrange them if all boys and girls…

Q: How many permutation can we make if we have 12 elements and use 4 at a time?

A: Given data:   The total numbers of elements are n=12. The numbers of elements used at a time are…

Q: supermarket wants to send codes for $0.25 off a bag of chips to its rewards program members. Each…

A: Given, a supermarket wants to send codes for $0.25 off abag at chips to its rewards program…

Q: Suppose a company needs temporary passwords for the trial of a new payroll software. Each password…

A: The objective of this question is to find out the total number of possible passwords that can be…

Q: Suppose each license plate in a certain state has three digits followed by three letters. The digits…

A: The objective of this question is to find out the total number of license plates that can be…

Q: how many ways can a party of 8 people be seated in a circular table if 3 of them insist on sitting s

A: Given data,In a party there are 8 peoplen=8how many ways can a party of 8 people be seated in a…

Q: 3. In how many ways can you arrange 5 books on a shelf from available 10?

A: The number of all combination of n things, taken r at  time is given by:

Q: If 4 marbles are picked randomly from a basket containing 5 blue marbles and 8 yellow marbles, in…

A: This is the problem of combinatorial.

Q: How many 13-letter words contain exactly 3 vowels? (For example, an 8-le with 5 vowels is…

A: There are total 26 letters in English alphabet and 5 are vowels and 21 are consonants.

Q: nhow many nights may a watch of 4 men be arranged by a security agency om a crew of 16 so that no…

A:

Q: Give 1 example of Permutation with Combination problem with solution.

A:

Q: Is there any derivation of the formula of permutation and combination?

A: Derivation for the formula of permutation and combination . Permutation : (Arrangement of r things…

Q: How many permutations can be made out of the letters in the word CAROLINE taken 4 at a time?

A: There are 8 letters in the word CAROLINE. We can take 4 letters from 8 letters in 8P4=8!(8-4)!=1680…

Q: Suppose that 9 people lost an average of 13.3 pounds over the course of the first month of being on…

A: 9 people lost 13.3 pounds on an average. Let w1,w2,...,w9 be the weight loss of the 9 people. Then…

Q: A shop has 6 types of candy. How many ways are there to select 24 pieces of candy with at least two…

A: The shop has 6 types of candy, so for each candy there are 6 ways of selection. 2 of each kind are…

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: 5) The number of 3 - digit numbers with repeats, that are multiples of 5 and less than 600 that can…

A: A three digit number should be made which is less than 600. The objective is to find the number of 3…

Q: In how many ways can a bag of three identical balls and four identical coins be formed from a group…

A: Given: Total number balls =12 Total number coins =12

Q: Every year a herd of buffalo increase by 50%. Suppose that at year 0 there are 60 buffalo, and each…

A:

Q: In a Teaching Center, 8/15 of the students are from Compulsory Secondary and the rest from…

A:

Q: A secret code for a bank vault consists of 2 letters, then 4 digits and then 4 more letters. How…

A: A code contains 2 letters, 4 digits and then 4 more letters.

Q: Find the number of distinguishable permutations of the word "VANQUISH".

A: Given word is "VANQUISH"    Total no. of letters=8    and no letter is repeated.

Q: 3 A recent survey concluded that of the teachers in a certain school district had at least 10 years…

A:

Q: Suppose a group of twelve (12) people consists of five (5) men and seven (7) women. How many…

A:

Q: In how many ways can a person choose three movies to watch from a collection of 7 suggested movies?

A: The formula for combination is nCr= n! / [r! (n – r)!] = [n (n – 1) … (n – r + 1)] / r!.…

Q: Many states have a lottery game, usually called Pick-4, in which you pick a four-digit number such…

A:

Set Theory

Every field in the present world involves a set. The theory of sets was developed by German mathematician Georg Cantor while working on the “problems of trigonometric series”.