Please help me???

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Ye Hai Luo

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Aug 5, 2021
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Question 1
(a) There are 6 students, Alfie, Ben, Carol, Dennis, Edward and Fenny
(i) In how many ways can these 6 students be seated in 5 chairs? (2 marks)
(ii) If Carol must sit in chair number 1, how many difference ways now? (3 marks)
(iii) If Dennis can sit anywhere except in chair no 1and Fenny must sit in chair no 3, how many difference
ways now? (4 marks)
(b) There are 6 girls and 7 boys in a club.
(i) In how many ways can we select a committee of 5 students? (2 marks)
(ii) In how many ways can we select a committee of 3 girls and 4 boys? (3 marks)
(iii) In how many ways can we select a committee of 4 students that at least one girl? (3 marks)
(iv) In how many ways can we select a committee of 4 students that at most one boy?
(3 marks)
 
Ye Hai Luo said:
Question 1
(a) There are 6 students, Alfie, Ben, Carol, Dennis, Edward and Fenny
(i) In how many ways can these 6 students be seated in 5 chairs? (2 marks)
(ii) If Carol must sit in chair number 1, how many difference ways now? (3 marks)
(iii) If Dennis can sit anywhere except in chair no 1and Fenny must sit in chair no 3, how many difference
ways now? (4 marks)
(b) There are 6 girls and 7 boys in a club.
(i) In how many ways can we select a committee of 5 students? (2 marks)
(ii) In how many ways can we select a committee of 3 girls and 4 boys? (3 marks)
(iii) In how many ways can we select a committee of 4 students that at least one girl? (3 marks)
(iv) In how many ways can we select a committee of 4 students that at most one boy?
(3 marks)
Click to expand...
a) name your variables - A (for Alfie), B (for Ben), C (for Carol), D (for Dennis), E (for Edward) and F (for Fenny)

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:


Please share your work/thoughts about this problem.
 
Ye Hai Luo said:
Question 1
(a) There are 6 students, Alfie, Ben, Carol, Dennis, Edward and Fenny
(i) In how many ways can these 6 students be seated in 5 chairs? (2 marks)
Click to expand...
How many choices do you have for the first chair? for the second? and so on.

Give it a try.

Do you know a name for this calculation?
 
Subhotosh Khan said:
a) name your variables - A (for Alfie), B (for Ben), C (for Carol), D (for Dennis), E (for Edward) and F (for Fenny)

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:


Please share your work/thoughts about this problem.
Click to expand...
230738562_2826255597498041_3058491745522617946_n.jpg
these were what i did, but my friends didn't agree my calculation step and said my answers were wrong so i don't know what to do already, and especially a)ii) and a)iii)
 
Ye Hai Luo said:
my friends said the questions has to use C not P
Click to expand...
They're wrong. But do you know why? What is the difference between combinations and permutations?

Ye Hai Luo said:
Question 1
(a) There are 6 students, Alfie, Ben, Carol, Dennis, Edward and Fenny
(i) In how many ways can these 6 students be seated in 5 chairs? (2 marks)
(ii) If Carol must sit in chair number 1, how many difference ways now? (3 marks)
(iii) If Dennis can sit anywhere except in chair no 1and Fenny must sit in chair no 3, how many difference
ways now? (4 marks)
Click to expand...
For (i) you used permutations, which is correct, since both the students and the chairs are distinct. (I'm assuming that "6 students be seated in 5 chairs" means that one doesn't sit, not that two sit in one chair. That isn't entirely clear.)

For (ii) you seem to show an awareness that one chair is already chosen, so there are only 5 left to place (but in 4 remaining chairs, not 5); why did you use 6! ?

For (iii) you haven't clearly shown your reasoning. But it looks like you are still thinking there are 6 chairs, assuming the blanks represent chairs. And what if D doesn't get a chair at all? (I don't know if it's saying that F must sit, or can only sit in #3.)

The problem could have been clearer.
 
Dr.Peterson said:
They're wrong. But do you know why? What is the difference between combinations and permutations?


For (i) you used permutations, which is correct, since both the students and the chairs are distinct. (I'm assuming that "6 students be seated in 5 chairs" means that one doesn't sit, not that two sit in one chair. That isn't entirely clear.)

For (ii) you seem to show an awareness that one chair is already chosen, so there are only 5 left to place (but in 4 remaining chairs, not 5); why did you use 6! ?

For (iii) you haven't clearly shown your reasoning. But it looks like you are still thinking there are 6 chairs, assuming the blanks represent chairs. And what if D doesn't get a chair at all? (I don't know if it's saying that F must sit, or can only sit in #3.)

The problem could have been clearer.
Click to expand...
Okay, noted. Thanks for help ☺️
 
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