In crayon box contains 2 green, 3 yellow and 4 blue crayons. In how many ways can one choose 3 crayons so that at least one yellow crayon is included?

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: A math teacher wishes to split a class of thirty students into groups. All groups will work on the…

A: Given data: Total students  = 30 To find: In how many ways can the teacher assign students to the…

Q: A quiz consists of 3 true-or-false questions.  In how many ways can a student answer the quiz?

A: Given that there are 3 true or false questions. Each question has 2 possible outcomes. That is true…

Q: In how many ways can 2 pizza toppings be chosen from 12 available toppings?

A: We have given that 2 pizza toppings be chosen from 12 available.

Q: Suppose you had 4 red checker pieces and 5 black checker pieces. How many ways can you arrange these…

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Q: How many 5 letter "words" can be formed if exactly 2 of the letters are vowels if repetition is…

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Q: How many numbers greater than 3000 can be form with the digits 0,2,3,4 a.  if repetition is not…

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

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Q: In a police departmets there are 7 policemen. If there are 7 districts that should be on patrol, how…

A: Given that total policemen, n= 7 And districts, r= 7

Q: A bag contains 5 apples and 3 oranges. If you select 4 pieces of fruit without looking, how many…

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

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Q: A license plate is to consist of 3 letters followed by 5 digits. Determine the number of different…

A: First, make all possible combinations of first 3 elements of the license plate, that is we need 3…

Q: An individual is going to paint the 5 toes of their right foot using one or two, but not three of…

A: An individual is going to paint the 5 toes of her right foot using one or two, but not three of the…

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: 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: How many outfits can be constructed with 1 shirt, 1 pants, and 1 tie from a wardrobe of 2 shirts, 5…

A: The given problem is based on combination {Because order doesn't matter}. The combination of…

Q: There are 7 Math books, 4 English books and 6 Filipino books on a shelf. How many ways can you…

A: Permutation: Permutation means finding a number of ways to arrange a specified number of distinct…

Q: If repetitions are not permitted, how many 3-digit even numbers can be performed from the six digits…

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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: A particular brand of shirt comes in 12 colors, has a male version and a female version, and comes…

A: Producer Rule: if one event can occur in m ways and a second event can occure in n ways the numbers…

Q: How many 2 – digit numbers can be formed from the four integers 1, 2, 3, and 4 if repetition is…

A: Given2-digit numbers to be formedNo.of integers =4           (1,2,3,4)

Q: How many numbers consisting of five different digits can be made from the digits (0, 1 , 2, 3, 4, 5,…

A: ConceptPermutation = n!/(n-r)!Given digits are 0,1,2,3,4,5,6,7,8,9

Q: In how many ways can 3 pizza toppings be choosen from 12 available toppings? Your answer is: -…

A: Given,            3 pizza toppings can be choosen from 12 availabe toppings.

Q: Determine the number of ways such that 5 men and 5 women be seated at a round table if no two women…

A: No. of men = 5  No. of women = 5

Q: How many ways to arrange 7 books on the shelf exist if two definite books are not placed together?

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Q: Suppose, you have 3 different caps, 4 different shirts, 3 different pants and 3 pairs of socks and 2…

A: Depends on given data total outfits 3x4x3x3x2= 216  No need to wear socks and caps So total ways…

Q: A jersey has two digit number.in how many ways can the number be arranged if 1)No double digit are…

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Q: There are 24 books on a shelf. How many ways are there to choose 10 of them so that no two of the…

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Q: A modernistic painting consists of triangles, rectangles, and pentagons, all drawn so as to not…

A: From given information consider the equations, x+y+z=40              ...13x+4y+5z=153…

Q: A student must take 4 courses. In how many ways can they do that if there are 8 courses and 1 is…

A: Solution

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: 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 combinations of three-digit numbers are possible with digits 2,4,6?

A: Given three digits are : 2 , 4  and 6 .  Combination of digits : _ _ _ (three places)  For the first…

Q: A computer password is to consist of three lower case letters followed by two digits. Determine how…

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Q: If 72 students which represent 2/3 of the class participated in the Alay Lakad, how many students…

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Q: Suppose that we have 10 numbered blocks, 2 RED, 3 BLUE, 4 GREEN, and one WHITE.  How many ways can…

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Q: How many nonsense words of 3 letters can be formed from the letters c, d, e, f and g if a.…

A: Permutation and combination used to calculate the number of possible ways to arrange or select a…

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: Assume that five men and five women are to sit in a row of ten chairs how many ways can these people…

A: Five men and five women are sitting in a row of ten chairs.

Q: four crayons be chosen from a bo

A: The selection of elements without arrangement can be represented by a combination of elements.…

Q: How many license plates are possible if they consist of 1 digit followed by 1 letter followed by 5…

A:

Q: How many 3-letter words can be made from the letters MATH if repetition of letters is allowed?…

A: We have given that a four letter word MATH from which we can made 3 letter words in two different…

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: If 4 Maths books are selected from 6 different Maths books and 3 English books are chosen from 5…

A: Solution  Given That,  If 4 Maths books are selected from 6 different Maths books and 3 English…

Q: Suppose there are 8 male professors and 5 female professors teaching a Math class. How many ways can…

A: Sum rule principle:   Let E1 denote the first event that an occur in m ways and then E2 denote the…

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

A: The given letters are FGHIJKL are have to find the no of three letterwords can be formed if…

Q: Dr. Volz gave an exam with 14 questions, but students only had to answer 10 of them. Suppose the…

A: We have to use combination formula. Formula : Crn = n!r!(n-r)!