Permutations (1 Viewer)

[Petinga]

1. Four men and four women are to be seated alternatley
a) in a row
b) at a round table. In how many ways can this be done?

2. Hiow many nuymbers greatewr than 4000 can be formed from 3,5,7,8,9? (REPITION NOT ALLOWED)\

3. In how many ways can the letters of the word PERMUTE be arranged if
a) first and last posiitons occupied by consonants
b) vowels and consonants occupy alternate places

4. How many numbners 0f 7 digits can be formed from the digits 1,2,3,4,5,6,,7 if:
a)numner begins 1 and ends with 2
b)there are not more than 2 digits between 1 and 2?

5. In how many wasy can 5 diff math books, 4 diff physics books and 2 diff chemisty books be arranged on a shelf if the books in each subject are together?

6. In how many ways can 3 men, 3 women, 3 boys be arraniged in a row if 3 boys to remain togeterr

7. How amny ways can letyers of PRINICPLE be arranged.

8. how manny ways can letters of PRECISION arranged? How many of these arrangements fo vowels occupy even places?

 

[pLuvia]

1a) 8! = 40320
b) 7! = 5040

3a)
4x3x5! = 1440
b) 4x3x3x2x2x1x1 = 144

4a) 5! = 120
b) 5! x 30 = 3600

7.
PRINCIPLE
9! / 2!x2! = 909720

 

[Boxxxhead]

1a) If they're steated alternatively, then it'd be 4! x 4!, then by 2!.. So 1152
1b) Since a table is (n-1)!, it'd be 4! x 3! .. So 144

2) Do 4 digit numbers first, so it'd be 4 x 4 x 3 x 2,
Then do 5 digit numbers, so it'd be 5 x 4 x 3 x 2 x 1, then add to get 216.

3a) 4 consonants, 3 vowels... so 4 x 3 x 5! = 1440, then you divide by 2! as there are two E's, equalling 720
3b) 4! x 3! / 2! = 72

4a) 1 x 1 x 5! = 120
4b) This takes a while, you gotta consider if there are no digits, 1 digits or 2 digits between them. So for no digits = (2!) x 6! = 1440
Then for 1 digit in between = (1 x 1 x 5 x 2!) x 5! = 1200
Then for 2 digits in between = (1 x 5 x 4 x 1 x 2!) x 4! = 960
Add the three to get 3600

5) Maths (5!) x Physics (4!) x Chem (2!), then x 3! to arrange different subjects to get 34560.

6) Three boys = 3!. then x by 7! = 30240

7) 9!, then divide by 2! for two I's and 2! for two P's = 90720

8) 9! divided by 2! =181440
Then for evenly placed vowels, 5! x 4! / 2! = 1440

 

[pLuvia]

Fark, I suck at permutations

 

[Boxxxhead]

Fark, I suck at permutations

Don't worry about it dude, many people suck at permutations and probability in general. There are numbers of people who perform exceptionally at maths, then falter in probability.