mathmath333
  • mathmath333
counting question
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
schrodinger
  • schrodinger
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
mathmath333
  • mathmath333
\(\large \color{black}{\begin{align} & \normalsize \text{In how many ways can the letters of the word PERMUTATIONS be arranged if the}\hspace{.33em}\\~\\ & \normalsize \text{ (i) vowels are all together }\hspace{.33em}\\~\\ & \normalsize \text{ (ii) there are always 4 letters between P and S.}\hspace{.33em}\\~\\ \end{align}}\)
rational
  • rational
How many vowels are there ?
mathmath333
  • mathmath333
all vowels are there

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

rational
  • rational
put them in a bag and call it \(\phi\)
rational
  • rational
how many ways can arrange the objects \(\{\phi, ~P, ~R, ~M,~T,~T,~N,~S\}\) ?
mathmath333
  • mathmath333
=(8/2)!
anonymous
  • anonymous
12!/(12-5)! for i?
rational
  • rational
you mean 8!/2 ?
mathmath333
  • mathmath333
ya this one
rational
  • rational
Yes, next unpack the bag, how many ways can you arrange 5 vowels ?
mathmath333
  • mathmath333
can vowels be repeated
rational
  • rational
what letters do you have in the bag ?
mathmath333
  • mathmath333
aeiou
rational
  • rational
they all are distinct, how many ways can you arrange them ?
mathmath333
  • mathmath333
5!
rational
  • rational
Yes, so the final answer is ?
mathmath333
  • mathmath333
8!*5!/2
rational
  • rational
looks good!
mathmath333
  • mathmath333
ok the next one
ikram002p
  • ikram002p
separated than the first condition ?
mathmath333
  • mathmath333
P and S are at distance of 4 places always
rational
  • rational
First find the number of ways of placing \(P, S\) : |dw:1439069671413:dw|
mathmath333
  • mathmath333
12*11
rational
  • rational
nope, try again
mathmath333
  • mathmath333
11
rational
  • rational
|dw:1439070002368:dw|
rational
  • rational
If one letter of {P, S} is at index 1, where can the other letter be ?
mathmath333
  • mathmath333
6
rational
  • rational
Yes, {P, S} can be mapped to {1, 6}
rational
  • rational
By sliding to right, you can see that {P, S} can take on locations : {1, 6} {2, 7} {3, 8} {4, 9} {5, 10} {6, 11} {7, 12} how many are they ?
mathmath333
  • mathmath333
7
rational
  • rational
and you can swap the locations, so there are 7*2 = 14 different ways to arrange {P, S}
rational
  • rational
Next, arrange remaining 10 letters
mathmath333
  • mathmath333
10!/2
rational
  • rational
Yes, so total num of permutations = 14(10!/2)
mathmath333
  • mathmath333
if the restriction of 4 places is not there then their are 10!/2 ways and the restrictions are their then there are 14*10!/2 ways but as the restrictions are more the the number of ways should decrease .
rational
  • rational
if the restriction is not there, then there are 12!/2 different permutations not 10!/2
mathmath333
  • mathmath333
ohk i see the difference :D
mathmath333
  • mathmath333
hmm this little silly doubts make my brain spin
rational
  • rational
its natural, my brain spins too :)
rational
  • rational
listing the possibilities and looking at the problem from alternative ways usually helps...
mathmath333
  • mathmath333
but in the way of learning its essential to get rid of the small doubts
rational
  • rational
haha! its good to ask questions there is an old saying : "there are no stupid questions, only stupid answers" remember that when asking a question which you feel is small/silly ;p
mathmath333
  • mathmath333
yes thumbs up!
mathmath333
  • mathmath333
remembering school days where teachers used to run after students after student asked questions

Looking for something else?

Not the answer you are looking for? Search for more explanations.