Brain Teasers
Wigan Smith
Whilst trekking through the jungles of Madadia, the intrepid explorer "Wigan Smith" discovers an isolated tribe of the legendary Kebab people. The Kebab people's written alphabet contains only six letters (call the letters A, B, C, D, E and F). The tribe has a fear against using the same letter twice in the same word, believing the great Gods of the "Chillisauce Volcano" will be angered. So it's never done.
If each different sequence of letters constitutes a different word in the language, what is the maximum number of six-letter words that the language can employ?
If each different sequence of letters constitutes a different word in the language, what is the maximum number of six-letter words that the language can employ?
Answer
The language can employ a maximum of 720 six-letter words.It is a simple permutation problem of arranging 6 letters to get different six-letter words. And it can be done in 6! ways i.e. 720 ways.
In other words, the first letter can be any of the given 6 letters (A through F). Then, whatever the first letter is, the second letter will always be from the remaining 5 letters (as same letter can not be used twice), and the third letter will always be from the remaining 4 letters, and so on. Thus, the different possible six-letter words are 6*5*4*3*2*1 = 720.
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