In how many ways can 6 differently shaped blocks be taken to arrange in a cabinet with 4 empty places?

Q: How many different committees are possible that consist of 5 women and 3 men selected from a group…

A: For a committee, arrangement does not matter so use the combination method.  We can select 5 women…

Q: How many ways are there to distribute eight balls into six distinct boxes with at least one ball in…

A: The balls are identical. In this case there are 8 balls and 6 boxes to be placed, so each box can be…

Q: c. How many ways can you choose 3 pieces from the 4 kings and queens (black king, white king, black…

A: Here, order matters. Therefore permutation rule can be applied. Permutation Rule: A permutation is…

Q: Compute how many different ways there are to color the faces of a cube so that three faces are red,…

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Q: If the goal keeper and defender should be selected from Class X that has 40 students for school…

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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: What is the total number of ways to allocate six unique objects among four crates, ensuring that…

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Q: How many 5 letter words can be formed if no letter is allowed to be used no more than once in a…

A: It is given that 5 letter words can be formed and also a word here is any combo of letters - it does…

Q: How many six-person lineups can be formed from a 10-player volleyball roster? (Every player plays…

A: There are 6 places that has to be filled by 10 players and any player can choose any position.

Q: Colombian license plates are made of 6 places. The rest 3 are letters, and the last 3 are numbers…

A: a) To calculate the number of possible license plates when you can repeat letters and numbers, you…

Q: A bag contains 7 black and 4 white balls. In how many ways can we draw from the bag groups of 5…

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Q: How many ways are there to arrange colored blocks if there are 5 red, 3 white, and 4 blue?

A: From the provided information, There are 5 red, 3 white, and 4 blue colors. Total = 5 + 3 + 4 = 12

Q: 8. Suppose Jack has 1 red ball, 1 orange ball, 1 blue ball, 1 yellow ball, 1 black ball and 1 green…

A: Given that  Jack has  Red ball = 1 Orange ball = 1 Blue ball  = 1 yellow ball = 1 black ball = 1…

Q: In how many ways can 7 children and 6 mother be arranged in a row so that:  No two children are sit…

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Q: Suppose any possible arrangement of 8 letters is considered a word and the letters are chosen from…

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Q: With a short time remaining in the​ day, a delivery driver has time to make deliveries at 5…

A: Given that, A delivery driver has time to make deliveries at 5 locations among the 9 locations.…

Q: In a shipment of  59 vials, only 14 do not have hairline cracks. If you randomly select 2 vials from…

A: Given that  Number of vials (n) = 59 Vials do not have hairline cracks = 14 Vials having hairline…

Q: 1. A farmer planted a crop of corn in one of his fields. There are 4816 stalks of com in equal rows.…

A: Total number of stalks of corn in the field, X=4816 stalks. Number of stalks of corn in each row,…

Q: Find the number of permutations of 4 distinct objects. There are permutations.

A: Permutation: Permutation is an arrangement  of items in a permanent order. In permutations  Orders…

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: How many ways can a committee of 4 be selected from a club with 22 members?

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

Q: A park bench can seat 3 people. How many seating arrangements are possible if 3 people out of a…

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

Q: An Uber XL can hold between 1 and 4 people. One September evening, 5 distinct and random people need…

A: According to the given information, An uber XL can hold between 1 and 4 people. On September evening…

Q: Show all work!

A: Step 1: Problem 6: To find the probability of winning either the first or second prize, we need to…

Q: In how many ways can three dogs, four cats, four rabbits and two pigs be arranged in a row so that…

A: Given,no.of dogs=3no.of cats=4no.of rabbits=4no.of pigs=2

Q: In how many ways can 7 male students be arranged in a row if Hanz and Fitch insist next to each…

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Q: In how many ways can 7 black and 7 white balls be distributed into 7 boxes so that there are exactly…

A: Given : 7 black and 7 white balls 7 B , 7 W Given boxes = 7  there are exactly 2 balls in each box…

Q: A contractor builds homes of  11 different models and presently has 6 lots to build on. In how many…

A: We have to find the different ways can he arrange homes on these 6 lots...

Q: A sales assistant is hanging 12 sweaters on a rack. He has 3 brown sweaters, 4 purple sweaters, and…

A: There are 12 sweaters, and there are 3 brown, 4 purple, and 5 white sweaters.To find the number of…