What is the number of ways in which the letters of the word table can be arranged so that the vowels occupy even places?

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?

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

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

Fark, I suck at permutations

Fark, I suck at permutations