0
$\begingroup$

Hello sorry i am a student who sucks at math i do have a father but can't be found nowhere for a simple question to ask i have no one but happy to found this site maybe someone out there could help me explain in a more detail way how this combinatorics works

How many arrangements can be made out of the letters of the word YIELD with the vowels not being separated

possible solution are:

20 24 48 52 58

can anyone explain then to me how it is solve so i can solve the other rest problem i am good at learning it's just that i just need to see a sample.

$\endgroup$
4
$\begingroup$

Consider the four blocks $Y$, $IE$, $L$ and $D$. These can be arranged in $4! = 24$ ways. Moreover the vowels in the vowels block can be arranged in $2! = 2$ ways. In total there are therefore $2 \cdot 24 = 48$ ways to arrange the letters.

Sometimes we consider $Y$ to be a vowel, in this case the blocks are $YIE$, $L$ and $D$, and a similar calculation yields an answer of $36$, so the problem setter probably did not consider $Y$ as a vowel.

| cite | improve this answer | |
$\endgroup$
  • $\begingroup$ sir that's nice thank you is it right the way i see it 4! = 4 x 3 x 2 x 1 = 24 then 2! = 2 x 1 = 2.. $\endgroup$ – Detective7 Sep 11 '14 at 9:57
  • $\begingroup$ @Detective7: Yep. $\endgroup$ – J. J. Sep 11 '14 at 10:05

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.