The number five-letter words containing 3 vowels and 2 consonants that can be formed using the letters of the word ; EQUATION so that the two consonants occur together, is

There are 5 vowels and 3 consonants in the word EQUATION'. Three vowels out of 5 and 2 consonants out of 3 can be chosen ${ }^5{C}_3{\times }^3{C}_2$ v..rays. So, there are ${ }^5{C}_3{\times }^3{C}_2$ groups each containing 3 consonants and two vowels. Now, each group contains 5 letters which are to be arranged in such a way that 2 consonants occur together. Considering 2 consonants as one letter, we have 4 letters which can be arranged in 4! ways. But, two consonants can be put together in 2! ,vays. Therefore, 5 letters in each group can be arranged in 4! x 2! ways.

$\therefore$ Required number of words  $=\left({ }^5{C}_3{\times }^3{C}_2\right)\times 4!\times 2!=1440$