How many words can be formed using all the letters of the word ‘NATION’ so that all the three vowels should never come together?

Step-by-step solution

The given word is 'NATION'. Total number of words that can be formed from given word 'NATION' = 6! 2! = 6 5 4 3 2! 2! =360 Now numbers of words that can be formed from given word 'NATION', so that all vowels never come together. aligned & =360- [4! 3! 2! ] & =360-[24 3] & =360-72=288 aligned Option (C) is correct.