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)
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
\(= 5! \times \frac{4!}{2!2!}\)
\(= 120 \times 6\)
\(= 720\)
\(=6!\)