Question 40
From the letters of the word “STATISTICS”, how many distinct 10-letter words can be formed such that no two S’s appear consecutively?
Solution
In the word STATISTICS, there are 3S, 3T, 2I, 1C and 1A.
3T, 2I, 1C and 1A can be arranged in $$\frac{7!}{3!2!}=420$$ ways.
After arranging these 7 letters, we get 8 gaps which can be filled by the 3S. This approach ensures that no two S come together.
Choosing 3 gaps out of these 8 for every arrangement can be done in 8C3 ways i.e. 56 ways.
Total number of 10 letter words that can be formed such that no 2 S come together are 56 * 420 = 23520.
