Question

counting question

Answer 1

\(\large \color{black}{\begin{align}
& \normalsize \text{In how many ways can the letters of the word PERMUTATIONS be arranged if the}\hspace{.33em}\\~\\
& \normalsize \text{ (i) vowels are all together }\hspace{.33em}\\~\\
& \normalsize \text{ (ii) there are always 4 letters between P and S.}\hspace{.33em}\\~\\
\end{align}}\)

Answer 2

How many vowels are there ?

Answer 3

all vowels are there

Answer 4

put them in a bag and call it \(\phi\)

Answer 5

how many ways can arrange the objects \(\{\phi, ~P, ~R, ~M,~T,~T,~N,~S\}\) ?

Answer 6

=(8/2)!

Answer 7

12!/(12-5)! for i?

Answer 8

you mean 8!/2 ?

Answer 9

ya this one

Answer 10

Yes, next unpack the bag, how many ways can you arrange 5 vowels ?

Answer 11

can vowels be repeated

Answer 12

what letters do you have in the bag ?

Answer 13

aeiou

Answer 14

they all are distinct, how many ways can you arrange them ?

Answer 15

5!

Answer 16

Yes, so the final answer is ?

Answer 17

8!*5!/2

Answer 18

looks good!

Answer 19

ok the next one

Answer 20

separated than the first condition ?

Answer 21

P and S are at distance of 4 places always

Answer 22

First find the number of ways of placing \(P, S\) :