Question

Counting Problem

Answer 1

\(\large \color{black}{\begin{align}
& \normalsize \text{How many words of 11 letters could be formed with } \hspace{.33em}\\~\\
& \normalsize \text{all the vowels present in even places, using all the } \hspace{.33em}\\~\\
& \normalsize \text{letters of the alphabet ?(without repetition) } \hspace{.33em}\\~\\
\end{align}}\)

Answer 2

what are your thoughts?

Answer 3

\(\large \color{black}{\begin{align}
& a.)\ ^{21}P_{6}\times 5! \hspace{.33em}\\~\\
& b.)\ 21! \hspace{.33em}\\~\\
& c.)\ ^{21}P_{5}\times 5! \hspace{.33em}\\~\\
& d.)\ ^{26}P_{8} \hspace{.33em}\\~\\
\end{align}}\)

Answer 4

i m confused on how to think here

Answer 5

those 5 places are blocked with 5 vowels,
which can be arranged among themselves in how many ways??

Answer 6

6 letters should be vowels and 5 letters non vowels

Answer 7

how many other letters are left?
in how many ways can you arrange those other letters in 6 places?

Answer 8

5 vowels, at places:
2,4,6,8,10

Answer 9

\(\large \color{black}{\begin{align}
& ^{6}P_{5}\ ways \hspace{.33em}\\~\\
\end{align}}\)

Answer 10

iis it correct

Answer 11

sorry for asking many questions at one time.

lets just concentrate on

5 places are blocked with 5 vowels,
which can be arranged among themselves in how many ways??

Answer 12

5! ways

Answer 13

good!
now forget about those 5 places, they are done

only 6 more places to go,
and how many options do we have?

hint : consonants

Answer 14

there are 6 places and 21 consonants remaining

Answer 15

and how can we arrange that?

Answer 16

\(\large \color{black}{\begin{align}
& ^{21}P_{6}\ ways \hspace{.33em}\\~\\
\end{align}}\)

Answer 17

\(\huge \checkmark \)

Answer 18

any more doubts? :)

Answer 19

yes

Answer 20

does u mean 1st option is correct

Answer 21

ok thanks

Answer 22

yes.
clear any doubts that you have in your mind ...