A drawer contains a dozen brown socks and a dozen black socks, all unmatched. A man takes socks out at random in the dark. a) How many socks must he take out to be sure that he has at least two socks of the same color?   b) How many socks must he take out to be sure that he has at least two black Socks?

Q: The 23 colleges of interest to a high school senior include 4 that are expensive (tuition more than…

A: Solution

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: If 5 cards are dealt from a standard deck of cards, how many different ways can three clubs and two…

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Q: In a standard deck of 52 cards, how many different four-card hands can be formed with at most 2…

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Q: A group of students were asked whether they like Mathematics, Physics, or both. If 456 like…

A: We want to find total number of students.

Q: If any seven digits could be used to form a telephone number, how many seven digit telephone numbers…

A: a) Given data, n=10 r=7 If any seven digits could be used to form a telephone number, how many seven…

Q: How many five-card poker hands containing exactly one pair are possible from a deck of 52 cards?

A: To find n(S), determine the number of ways to choose five-card hands from a pack of 52 cards.…

Q: If a person can select five books from a list of ten, how many different combinations are there?

A: Given data: The total numbers of books are n=10. The number of books selected is r=5. The expression…

Q: Given a deck of 52 playing cards, in how many ways can a hand of 5 cards be dealt such that all are…

A: Given: The total number of cards in a deck is 52. The total number of the numbered cards in a deck…

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Q: A survey of 310 adults found that during the last year, 90 traveled by plane but not by train, 75…

A:

Q: A jar contains four white balls, eight black balls, and six red balls. In how many ways can two…

A: Given :Total number of balls in a Total number of white balls = 4 Total number of black balls = 8…

Q: Out of 9 children, in how many ways can a family have at least 1 girl?

A: We have given that, 9 children i.e. n=9 and family have at least 1 girl i.e. r=1   Combination…

Q: In a deck of 52 playing cards, how many 4-card hands are there that are made up of only red cards?

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Q: In a survey of 251 professional athletes, it was found that 125 of them owned a convertible, 99 of…

A: Let us denote C=convertible, T=giant screen TV, S=sporting good storeGiven that:n(C)=125, n(T)=99,…

Q: b) Suppose that repetition of letters is pemitted, How many 6 letter can be fomed from the letters?

A: Now we have to calculate ,how many 6 letter can be formed if repetition is permitted.

Q: A sporting goods store has fourteen lines of snow skis, eight types of bindings, eight types of…

A: It is given that, a sporting goods store has fourteen lines of snow skis, eight types of bindings,…

Q: A sporting goods store has thirteen lines of snow skis, eight types of bindings, eight types of…

A: Consider the given information:  There are 13 snow skies, 8 bindings, 8 boots and 4 types of poles.…

Q: 2. If you have 7 types of candy, how many pieces of candy would you have to guarantee that you had…

A:

Q: If 5 cards are dealt from a standard deck of​ cards, how many different ways can three spades and…

A: 5 cards are dealt from a standard deck of​ 52 cards. There are 13 spade cards. Therefore number of…

Q: The pool of students in a calculus class consist of 22 sophomore and 8 freshmen. If seven students…

A: (a) Determine the number of different groups of seven students can be selected. The number of…

Q: A golf-course architect has six linden trees, five white birch trees, and three bald cypress trees…

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Q: b.How many cards must be selected from a standard deck of 52 cards to guarantee that at least 5…

A:

Q: If radio station call letters must begin with either the letter K or W and must include either two…

A: Given information Letter can start with letter K or W and include either two or three additional…

Q: in how many ways can a hand of 5 cards be dealt such that 2 are black and 3 red cards?

A: Given:  There are 52 cards on the deck. There are 26 red and 26 black cards on the deck. Formula…

Q: Of 100 employees of a store located in downtown Boston, 36 people take the subway to work, 24 take…

A:

Q: 1. In your drawer, there are 6 identical pairs of purple socks, 7 identical pairs of polka dot…

A:

Q: In a survey of 105 people, it was found that 40 have lived only in New York, 35 have lived only in…

A: Given, In a survey of 105 people, it was found that 40 have lived only in New York,  35 have lived…

Q: A rental car company has 14 available cars while on its lot and 3 customers waiting in the office.…

A:

Q: How many people used two modes of transportation if 1978 took public transit, 1494 drove, 818…

A: Given Information: People who took public transit = 1978 People who drove = 1494  People who cycled…

Q: From a group of 10 men and 5 women, how many committees of size 5 are possible? a.) With no…

A: Given From a group of 10 men and 5 women, how many committees of size 5 are

Q: A cargo ship unloaded a shipment of 12 photocopy machines that contains 3 defective units. In how…

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Q: In a survey of 153 pet owners, 74 said they own a dog, and 36 said they own a cat. 5 said they own…

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Q: 8. The captain of a baseball team assigns himself to the 6th place in the batting order. In how many…

A: When you arranging elements (r) from orders list (n), Permutation is a matter of orders while, the…

Q: The 23 colleges of interest to a high school senior include 4 that are expensive (tuition more than…

A:

Q: how many hands of 33 cards can be made, where all cards are of the same suit?

A:

Q: had a number of colored marbles in a bag. - of the marbles were red, of the remaining marbles were…

A: Simple calculation

Q: The 22 colleges of interest to a high school senior include 7 that are expensive (tuition more than…

A: Given Data: n=22 n(E)=7 n(F)=7 n(EUF)=5

Q: From a club of 16​people, in how many ways can a group of six members be selected to attend a​…

A:

Q: If there are 13 employees in a club, in how many ways can they choose a dishwasher and a bouncer?

A: Given information- We have given that there are 13 employees in a club. They want to choose a…

Q: A survey of 275 adults found that during the last year, 70 traveled by plane but not by train, 40…

A: Introduction:Denote the following events for the different modes of travel:P: Plane,T: Train,B:…

Q: A man has eight shirts and five ties. Assuming that they all match, how many different shirt-and-tie…

A: Given,            A man has eight shirts and five ties.

Q: In a survey of 94 pet owners, 33 said they own a dog, and 71 said they own a cat. 31 said they own…

A: Given ,  In a survey of 94 pet owners, 33 said they own a dog, and 71 said they own a cat. 31 said…

Q: Of the first 5 vehicles in the teacher’s parking lot last Tuesday, 2 of them were minivans. Based on…

A: 48

Q: A cookie jar contains 10 cookies - 4 are chocolate chip, 3 are almond, 2 are oatmeal and 1 is a high…

A: Answer -  Total cookies = 10  Chocolate chips = 4 almond = 3 oatmeal = 2  high fibre cookie = 1

Q: Find the number of full houses in a poker hand, that is, the number of poker hands with three of a…

A: Let there be 4C3 =4 by choosing the 3 cards of the same typesand 4C3 =6  by choosing…

Q: From a group of 18 customers, 4 are to be chosen to receive a special gift. Assuming that the order…

A: The number of groups of 4 customers can be chosen is,

Q: Eight runners are hoping to take part in a race, but the track has only six lanes. In how many ways…

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Q: In a survey of 80 university students, 58 had taken mathematics course, 40 had taken biology course,…

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Q: If there are 10 people and only 6 chairs are available, in how many ways can they be seated?

A: