Permutations / Combinations Questions? (1 Viewer)

[beve]

I'm studying for my Extension Maths assessment next week. Can anybody point me towards some questions on Permutations & Combinations? I only have a sheet or two on them... =(

 

[Aerath]

What about your textbooks? =\

 

[beve]

Well, its not in the prelim textbook and I dont have the HSC one. We have Maths In Focus textbooks. =/

 

[tacogym27101990]

the preliminary excel book does perms and combs pretty good. or you could get something like that phoenix past paper questions as you can then practise all the topics

 

[bored of sc]

Here's some questions for you (taken from Fitzpatrick):

Permutations

1. How many different arrangements can be made by taking 3 of the letters of the word Sunday?

2. In how many ways can 5 boys be arranged in a row?

3. In how many ways can a first, second and third prize be awarded in a class of 8 students?

4. How many 5-digit numbers can be formed from the digits 2,3,5,6,8,9 if no digit can be used more than once? How many even numbers can be formed?

7. In how many ways can 4 consonants and 3 vowels be arranged in a row
(a) so that the 3 vowels are always together?
(b) so that the first and last places are occupied by consonants?

17. If 6Pr = 120, find the value of r.

25. In how many ways can the letters of precision be arranged? In how many of these arrangements do vowels occupy even spaces?

27. How many arrangements of the letters in tomato are there, if the letters o are to be separated?

29. In how many ways can 4 people be accommodated if there are 4 rooms available?

30. In how many ways can 8 people be seated in a 8-oared boat if three can row only on the stroke side and 3 can row only on the bow side?

33. In how many ways can 5 men and 5 women be arranged in a circle so that the men are separated? In how many ways can this be done if two particular women must not be next to a particular man?

34. How many arrangements of the letters of the word PARRAMATTA are possible?


Combinations

1. In how many ways can 3 books be selected from 8 different books?

2. In how ways can a set of 2 boys and 3 girls be selected from 5 boys and 4 girls?

3. How many different selections can be made by taking 3 of the digits 4,5,6,7,8,9?

4. In how many ways can a committee of 4 men and 5 boys be formed from 8 men and 7 boys?

8. In how many ways can 3 cards be selected from a pack of 52 playing cards if
(i) at least one of them is an ace?
(ii) not more than one is an ace?

10. A committee of 7 politicians is chosen from 10 liberal members, 8 labor members and 5 independents. In hwo many ways can this be done so as to include exactly 1 independent and at least 3 liberal members and at least 1 labor member?

13. From 4 oranges, 3 bananas and 2 apples, how many selections of 5 pieces of fruit can be made, taking at least one of each kind?

16. In how many ways can a jury of 12 be chosen from 10 men and 7 women so that there are at least 6 men and not more than 4 women on each jury?

17. In how many ways can a set of 3 or more be selected from 9 people?

23. How many words (arrangements of letters), containing 3 consonants and 2 vowels, can be formed from the letters of the word promise?

25. If nC6 = nC4, find the value of n.

27. In how many ways can 9 books be distributed amongst a man, a woman and a child, if the man receives 4, the woman 3 and the child 2?

29. In how many ways can 8 girls be divided into 4 sets of 2?

 

[lyounamu]

Here's some questions for you (taken from Fitzpatrick):

Permutations

1. How many different arrangements can be made by taking 3 of the letters of the word Sunday?

2. In how many ways can 5 boys be arranged in a row?

3. In how many ways can a first, second and third prize be awarded in a class of 8 students?

4. How many 5-digit numbers can be formed from the digits 2,3,5,6,8,9 if no digit can be used more than once? How many even numbers can be formed?

7. In how many ways can 4 consonants and 3 vowels be arranged in a row
(a) so that the 3 vowels are always together?
(b) so that the first and last places are occupied by consonants?

17. If 6Pr = 120, find the value of r.

25. In how many ways can the letters of precision be arranged? In how many of these arrangements do vowels occupy even spaces?

27. How many arrangements of the letters in tomato are there, if the letters o are to be separated?

29. In how many ways can 4 people be accommodated if there are 4 rooms available?

30. In how many ways can 8 people be seated in a 8-oared boat if three can row only on the stroke side and 3 can row only on the bow side?

33. In how many ways can 5 men and 5 women be arranged in a circle so that the men are separated? In how many ways can this be done if two particular women must not be next to a particular man?

34. How many arrangements of the letters of the word PARRAMATTA are possible?


Combinations

1. In how many ways can 3 books be selected from 8 different books?

2. In how ways can a set of 2 boys and 3 girls be selected from 5 boys and 4 girls?

3. How many different selections can be made by taking 3 of the digits 4,5,6,7,8,9?

4. In how many ways can a committee of 4 men and 5 boys be formed from 8 men and 7 boys?

8. In how many ways can 3 cards be selected from a pack of 52 playing cards if
(i) at least one of them is an ace?
(ii) not more than one is an ace?

10. A committee of 7 politicians is chosen from 10 liberal members, 8 labor members and 5 independents. In hwo many ways can this be done so as to include exactly 1 independent and at least 3 liberal members and at least 1 labor member?

13. From 4 oranges, 3 bananas and 2 apples, how many selections of 5 pieces of fruit can be made, taking at least one of each kind?

16. In how many ways can a jury of 12 be chosen from 10 men and 7 women so that there are at least 6 men and not more than 4 women on each jury?

17. In how many ways can a set of 3 or more be selected from 9 people?

23. How many words (arrangements of letters), containing 3 consonants and 2 vowels, can be formed from the letters of the word promise?

25. If nC6 = nC4, find the value of n.

27. In how many ways can 9 books be distributed amongst a man, a woman and a child, if the man receives 4, the woman 3 and the child 2?

29. In how many ways can 8 girls be divided into 4 sets of 2?

Wow, you are bloody awesome!!!

Writing that all out would have taken you some time. Well done mate, you are a true legend. (even though I already have Fitz, I am just inspired by your work here).

 

[beve]

Here's some questions for you (taken from Fitzpatrick):

Permutations

1. How many different arrangements can be made by taking 3 of the letters of the word Sunday?

2. In how many ways can 5 boys be arranged in a row?

3. In how many ways can a first, second and third prize be awarded in a class of 8 students?

4. How many 5-digit numbers can be formed from the digits 2,3,5,6,8,9 if no digit can be used more than once? How many even numbers can be formed?

7. In how many ways can 4 consonants and 3 vowels be arranged in a row
(a) so that the 3 vowels are always together?
(b) so that the first and last places are occupied by consonants?

17. If 6Pr = 120, find the value of r.

25. In how many ways can the letters of precision be arranged? In how many of these arrangements do vowels occupy even spaces?

27. How many arrangements of the letters in tomato are there, if the letters o are to be separated?

29. In how many ways can 4 people be accommodated if there are 4 rooms available?

30. In how many ways can 8 people be seated in a 8-oared boat if three can row only on the stroke side and 3 can row only on the bow side?

33. In how many ways can 5 men and 5 women be arranged in a circle so that the men are separated? In how many ways can this be done if two particular women must not be next to a particular man?

34. How many arrangements of the letters of the word PARRAMATTA are possible?


Combinations

1. In how many ways can 3 books be selected from 8 different books?

2. In how ways can a set of 2 boys and 3 girls be selected from 5 boys and 4 girls?

3. How many different selections can be made by taking 3 of the digits 4,5,6,7,8,9?

4. In how many ways can a committee of 4 men and 5 boys be formed from 8 men and 7 boys?

8. In how many ways can 3 cards be selected from a pack of 52 playing cards if
(i) at least one of them is an ace?
(ii) not more than one is an ace?

10. A committee of 7 politicians is chosen from 10 liberal members, 8 labor members and 5 independents. In hwo many ways can this be done so as to include exactly 1 independent and at least 3 liberal members and at least 1 labor member?

13. From 4 oranges, 3 bananas and 2 apples, how many selections of 5 pieces of fruit can be made, taking at least one of each kind?

16. In how many ways can a jury of 12 be chosen from 10 men and 7 women so that there are at least 6 men and not more than 4 women on each jury?

17. In how many ways can a set of 3 or more be selected from 9 people?

23. How many words (arrangements of letters), containing 3 consonants and 2 vowels, can be formed from the letters of the word promise?

25. If nC6 = nC4, find the value of n.

27. In how many ways can 9 books be distributed amongst a man, a woman and a child, if the man receives 4, the woman 3 and the child 2?

29. In how many ways can 8 girls be divided into 4 sets of 2?

Thankyou so much. =)

 

[bored of sc]

No worries. I you would like answers/working PM me.