Explain why the number of combinations of n items taken rat a time can be computed by - r!

Q: How many arrangements are there of the letters of the word MATHEMATICS in which all the vowels…

A:

Q: In how many ways can the letters of the word HORRAR be arranged if vowels are together?

A: Given information- We have given the letters of the word- HORRAR We have to find a number of ways to…

Q: How many false positives were there among these 189 people? Explain the meaning of a false positive…

A: Introduction - Reasons for false positives :- Non-specific results cross-reactions problems in…

Q: How many 5-digit numbers can you make using the digits 1-8 if repetition is allowed?

A:

Q: Suppose a standard six-sided die is rolled and you receive $4.50 for every dot showing on the top of…

A: In order to make it a fair game , the average winning should be equal to the average cost of the…

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: How many ways can the Blue, Red, and Yellow ribbons be awarded to the 9 participants of a 10k race?

A: Given,Total no.of participants=9no.of ribbons=3

Q: How many ways can the top four cash prices be awarded in a lottery that sold 150 tickets if each…

A: here given scenario is with replacement ,

Q: Find the number of the permutation of 8 different things taken 3 at a time

A:

Q: How many possible results are there that A finished the first, B finished the second, and C finished…

A: SIX STUDENTS ARE SELECTED TO RUN 100 METER SPRINT. ASSUME THAT THEY ARE EQUALLY GOOD AND RESULT ARE…

Q: A teacher wants to assign 4 different tasks to her 4 students. In how many possible ways can she do…

A: Solution

Q: In your school, 40% of students watch TV at night. You randomly ask 5 students every day if they…

A:

Q: A car insurance company claims that 92% of its customers are happy with their service. You randomly…

A: Given,   The sample proportion is,

Q: How would I solve the following problem: Of five letters (A, B, C, D, and E), two letters are to be…

A: Ans#- Given,           Five letters (A, B, C, D, and E), two letters              are to be selected…

Q: In how many ways can you distribute n pennies to k children if each child is supposed to get at…

A:

Q: In how many ways can an adviser assign a different task to 9 students from a class of 15?

A: Here we need to assign a different task then we would use combination.   Combination formula: C(n,r)…

Q: 3. Suppose 1500 runners are in a race. How many ways could the runners finish in 1*, 2nd and 3rd…

A:

Q: The Knightrola Lottery has been updated to allow choosing 6 numbers out of 63 on a $1 ticket.…

A: Cost of 1 lottery ticket is $1. Total number in the lottery are 63. Total selected number for 1…

Q: How many 6-places license plates are possible if he first 3 places re to be occupied by letters and…

A: Given data: How many 6-places license plates are possible if he first 3 places are to be occupied by…

Q: How many combinations are possible? Assume the items are distinct. 9 items chosen 6 at a time…

A: According to the combination rule, if r distinct items are to be chosen from n items without…

Q: how many combinations are possible? assume the items are distinct. 16 items chosen 16 at a time

A: Only one combination is possible.

Q: How many combinations are possible? Assume the items are distinct. 5 items chosen 3 at a time…

A:

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

A:

Q: Question1:-If 6 seats are empty in a train box and two man entered in this coach than they seated…

A: Hi there! Thanks for the questions, since there are multiple questions we have solved the first…

Q: It's all about PERMUTATION - I'm how many different ways can 5 bicycles be parked if there are 7…

A: Given: n=7r=5 The number of ways 5 bicycles be parked in 7 available parking spaces is obtained as…

Q: How many ways are there to put 5 balls in 2 boxes if the balls are distinguishable and the boxes are…

A: Total number of distinct boxes=n=2 Total number of distinct balls=r=5

Q: How many ways can you have a 6-digit passcode on your phone if you start with a 9 and none of the…

A: We need to find the number of ways to have a 6-digit passcode, given that the first digit is 9 and…

Q: How many different words (including nonsense words) can you make by rearranging the letters of the…

A:

Q: How many ways can a person toss a coin 15 times so that the number of heads is between 8 and 13…

A: Since , the coin is tossed 15 times. Our aim is to find the number of heads is between 8 and 13…

Q: In how many ways can a student choose to do 5 questions out of 11 on a test?

A: The question is based on permutation. We need to find the number of ways a student can choose 5…

Q: How many 4-digit numbers can you make using the digits 1-5 if repetition is allowed? *

A: We have to find the number of 4-digit numbers that can be formed using the digits 1,2,3,4,5.The…

Q: How many ways are there for 6 people sitting around a circular table to pick from 12 entrees so that…

A:

Q: How many 5-digit numbers can you make using the digits 1-8 if repetition is allowed? *

A: Introduction: It is required to find the number of possible 5-digit numbers that can be made using…

Q: Suppose a standard six-sided die is rolled and you receive $3.00 for every dot showing on the top of…

A: Given Data: The amount recieve for every dot is: x=$3.00 The standard six sides die, has 1, 2, 3, 4,…

Q: 1 2 3 4

A:

Q: Find the number of ways in which 9 different computer games can be shared out between Wainah, Jingyi…

A: Here there are 9 different computer games that can be shared between Wainah (W), Jingyi (J) and Hebe…

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: Casino has a new game that uses 10 identical decks of cards mixed into 1 megadeck. How many 10 card…

A: A deck consists of 52 cards. Total cards in 1 megadeck that uses 10 identical decks of…

Q: in how many different ways could Dopey not be between Grumpy or Sleepy

A: Grumpy is second from the right and Sleepy is third from the left. Total positions where Dopey can…

Q: 6. How many ways can my daughter put 50 pairs of shoes on 4 dolls ?

A: It is given that, We have 50 pairs of shoes and there are 4 dolls. We know that if n object can be…

Q: How many combinations are possible? Assume the items are distinct. 19 items chosen 19 at a time…

A:

Q: what is the best prediction for the number of times a coin will land on heads and a spinner with…

A: According to the provided data, the number of times a coin is flipped and a spinner spin is 200.The…

Q: Suppose that 33% of McMaster undergraduate students are in their first year. President David Farrar…

A: It is given that p=0.33.

Q: How children in the exposed group have the number of finger-wrist taps in the dominant many hands…

A: Reviewing information, 2 groups are given with box plot

Q: Suppose a standard six-sided die is rolled and you receive $2.50 for every dot showing on the top of…

A: When a six-sided die is rolled the probability of getting each number is 1/6.  1 dot is present In…

Q: How many ways are there to select 5 cookies from a jar containing 3 types when repetition is…

A: Theorem-  there are C(n+r-1 , r) ways of choosing r-combination from a set of n elements when…

Q: How many ways can my daughter put 50 pairs of shoes on 4 dolls?

A: Combination :  The number of ways to choose a sample of k elements from a set of n distinct objects…

Q: How many four-digit numbers can be made from the digits 1 to 6 if repetition is allowed?

A: Number of four digit can be made from digits  1 to 6 :