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Find the number of arrangements of the letters of the INDEPEND

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Find the number of arrangements of the letters of the INDEPENDENCE. In how many of these arrangements,(i) do the words start with P(ii) do all the vowels always occur together(iii) do the vowels never occur together(iv) do the words begin with I and end in P?

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Find the number of arrangements of the letters of the INDEPENDENCE. In how many of these arrangements,(i) do the words start with P(ii) do all the vowels always occur together(iii) do the vowels never occur together(iv) do the words begin with I and end in P?

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Text solutionVerified

Solution: total arrangements =

\frac{12 !}{3 ! 2 ! 4 !}

(i)

P - - - - - - - - - - -

= \frac{11 !}{3 ! 2 ! 4 !}

(ii)

= \frac{8 !}{3 ! 2 !} \cdot \frac{5 !}{4 !}

(iii)

\frac{12 !}{3 ! 2 ! 4 !} - \frac{8 ! 5 !}{3 ! 2 ! 4 !}

(iv)

I - - - - - - - - - - P

= \frac{10 !}{3 ! 2 ! 4 !}

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Question Text	Find the number of arrangements of the letters of the INDEPENDENCE. In how many of these arrangements,(i) do the words start with P(ii) do all the vowels always occur together(iii) do the vowels never occur together(iv) do the words begin with I and end in P?
Answer Type	Text solution:1
Upvotes	150

Find the number of arrangements of the letters of the INDEPENDENCE. In how many of these arrangements,(i) do the words start with P(ii) do all the vowels always occur together(iii) do the vowels never occur together(iv) do the words begin with I and end in P?

Text solutionVerified

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