Count the number of strings of m 0s and n 1s that have exactly k blocks of consecutive 1s.

Q: The number of possible combinations if r objects are taken from n items is nCr =________.

A: The concept of combination is applied when following conditions are satisfied: a) Repetition is not…

Q: Bonita purchases 1225 white bouncy​ balls, 952yellow bouncy​ balls, and 504 orange bouncy balls. He…

A: Find the H.C.F of 1225, 952 and 504 that is 7 no of bags we have.

Q: There are 20 seats in the front row of a theater. Each successive row contains two more seats than…

A: The number of seats in the first row =20 Since each successive row contains two more seats than the…

Q: When a carton of apples were packed into bags of 4, there would be 3 apples left over. When the same…

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Q: . Bricks are stacked in 20 rows such that each row has a fixed number of bricks more than the row…

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Q: Suppose that 9 female and 4 male applicants have been successfully screened for 7 positions. In how…

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

Q: A theater has 25 seats in the first row and 35 rows in all. Each successive row contains one…

A: From the given information, it is observed that First row - 25 seats 2nd row - 26 seats.  (25+1) 3rd…

Q: There are 20 seats in the front row of a theater. Each successive row contains two more seats than…

A: There are 20 seats in the front row of a theater. Each successive row contains two more seats than…

Q: an auditorium has 45 seats in the 1st row, 52 seats in the 2nd row, 59 seats in the 3rd row, and so…

A: Given 45,52,59,............ To find : Number of seats in 35th row Given expression is in…

Q: library has an average of 510 visitors on Sunday and 240 on other days. The average number of…

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Q: A roller coaster has 3 trains with 8 rows per train. Riders stand in rows of 4, for a total of 32…

A: A fraction is a number in the form xy (where x and y are both integers and y≠0). In the above number…

Q: Four married couples have bought 8 seats in the same row for a concert. In how many different ways…

A: The number of ways to arrange r objects selected from n distinct objects is given by permutation.…

Q: What is the conjugate of the partition n = (n – k)+k, where n 2 2 and 1<k< [n/2]?

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Q: 5. Assume that each scoop can only hold a maximum of 8 pieces and a minimum of 2. How many ways are…

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Q: A person is knitting a baby blanket that will consist of four triangles arranged to form a square.…

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Q: Find the number of possible combinations of the letters w, x, y and z if the letters are taken 2 at…

A: We have to use combination formula to find the solution.

Q: For every 100 ticket buyers at a concert, the band expects to sell 27 T-shirts.

A: Given: For every 100 ticket buyers at a concert, The band expects to sell 27 T-shirts.

Q: Determine how many rows are in the corner section of a stadium containing 3920 seats if the first…

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Q: A group of 9 people consisting of 4 mothers and 5 children bought tickets for the cinema in the same…

A: A group of 9 people consisting of 4 mothers and 5 children bought tickets for the cinema in the same…

Q: You have 7 purple corn kernels, and 2 yellow corn kernels. (a) If you line them up in a row, how…

A: Permutation: the permutation is determining the number of possible arrangements in a set when the…

Q: A movie theater has 180 seats. How many rows of seats does it have if the first row has 12 seats and…

A: Given,         A movie theater has 180 seats. The first row has 12 seats and each succeeding…

Q: A tennis player keeps track of the number of successful first serves he makes. During the first 8…

A: After x successful serves, his total number of serves is going to bex+8, as he had already served 8…

Q: In a group of students, 65 likes red, 45 likes blue, 42 likes green, 20 likes red and blue, 25 likes…

A: Let R be the set of students liking the red color.  Let B be the sets of students liking the blue…

Q: Cells B1, C1, and D1 contain the values Seat1Row1, Seat1Row2, and Seat1Row3. Of cells B1,C1, and D1…

A: Given, Cells B1, C1, and D1 contain the values Seat1Row1, Seat1Row2, and Seat1Row3. Of cells B1,C1,…

Q: Find in how many ways can two admirals, three generals, and four lieutenants can be seated in a row…

A: Total seats = 9 Admirals =2 Generals=3 Lieutenants =4

Q: If there are x teams in a league and each team plays every other team twice, then the total…

A: Quadratic equation : A quadratic equation is any equation that can be rewritten in standard form as…

Q: Suppose that the number of students in a class increase by 2, the number of ways they may be…

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Q: 2. Assume that you have lots of pennies and nickels and you start arranging them in rows of 8 coins.…

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Q: The first ten rows of seating in a certain section of a stadium have 30 seats, 32 seats, 34 seats,…

A: Given: he first ten rows of seating in a certain section of a stadium have 30 seats, 32 seats, 34…

Q: How many children are there in a family wherein each girl has as many brothers as sisters, but each…

A: Let assume Number of sister = x Number of brother = y

Q: Mrs. Dronamraju has 30 tall plants. Fifteen of her plants have a height of 1.60 m and the remaining…

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Q: Two integers, a and b, have a product of 48. What is the least possible sum of a and b? The least…

A: Answer is a+b= -49. Explanation is given below...

Q: How many combinations are possible? assume the Items are distinct. 5 items chosen 2 at a time

A: C(n,r) = n! /{r! (n-r)!}

Q: in a baseball league consisting of 10 teams plays each of the other teams exactly three times . How…

A: Combination formula : nCr = n! /(n-r)! r!

Q: Apple has 252 sales repsin order to sell its apple watches.  Each to be assigned to 1 of 4 marketing…

A: Assume number of sales repsin in team2 be x and in team 4 be y So, number of sales repsin in team 1…

Q: A medical student has to work in a hospital for five days in January.  However, he is not allowed to…

A: there are 31 days in January Out of 31 days , student has to work 5 days therefore the non working…

Q: how many times can you put 8 people in groups of 4

A: Here use combination

Q: There are four students working on a project in math class. Miguel has completed 1/8 of the project,…

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Q: Maximize 2x, + x, + x, subject to x, + 5x, + x, s 5 3x, + 2 x, + x, < 9 5x, + 4 x, + 2x, s 10

A: (i) Solution of Linear Programming Problem via Simplex Method: 1. As the constraint 1 is of type '≤'…

Q: A fence is composed of x posts, each of which is 4 cm wide. If there is 6 cm of space between each…

A: The solution is given below.

Q: Peter must select 3 electives from a group of 8 courses. If all 8 of these courses are available…

A: Given Information: Peter must select 3 electives from a group of 8 courses. If all 8 of these…

Q: 2. In a basketball league consisting of 10 teams, each team play each of the other teams exactly…

A: Given information: Total teams=10 Each team of the other teams exactly three times.

Q: 20) Show that the sum of two consecutive integers is always odd.

A: Let x be any integer. Then its consecutive integer can be written as x+1.

Q: Jim  is designing stripes with five parallel colors on a piece of cloth. How many stripes can jim…

A: Given information: Jim  is designing stripes with five parallel colours on a piece of cloth. Number…

Q: be run under the building. If these two blocks must always be next to each other, how many s can the…

A: Given Here we have 7 blocks ,but we  have to keep 2 perticular blocks together. So we have to…

Q: Nonie has 2 blue candies for every 1 red candy. after he eats 1 of the blues and 2 of the reds,…

A: We have to find with how many candies did nanie start.

Q: Richard purchased 245 white bouncy balls, 238 yellow bouncy balls, and 84 orange bouncy balls. He…

A: Given that, the number of white balls is 245, the number of yellow balls is 238 and the number of…

Q: How many blocks would be needed to build a stack like the one shown In the figure If the bottom row…

A: Given that bottom row has 21 blocks. On going from bottom to top, number of blocks are reduced by 1.…

Q: A coin is tossed 3 times. What is the total number of all possible outcomes if there is exactly two…

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