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in Probability Distribution by (15 points)
edited ago by

in how many ways can the word BRAZILLIAN be arranged if the vowels and consonents are arranged in alternative position

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1 Answer

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Vowels in word BRAZILIAN are A, I, I & A.

Consonants in word BRAZILIAN are B, R, Z, L & N.

Total 4 vowels and 5 conssonant.

If they are arranged in alternative position, which only can happen if word start with a consonant. (∵ 5 > 4)

C V C V C V C V C

There are 5 consonant, no. of ways to arranged them = 5! = 120

There are 4 vowels (A, I, I & A)

no. of ways to arranged them = \(\frac{4!}{2!2!}= \frac{24}6\)

∴ Total no. of ways to arrange word BRAZILIAN is vowels & consonants are arranged in alternative position 

\(= 5! \times \frac{4!}{2!2!}\)

\(= 120 \times 6\)

\(= 720\)

\(=6!\)

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