Question 3

How many words can be formed by re-arranging the letters of the word PROBLEMS such that P and S occupy the first and last position respectively?

1. 8! / 2!
2. 8! - 2!
3. 6!
4. 8! - 2*7!
5. 6! * 2!

The correct Answer is 6! and the correct Choice is (C).

'PROBLEMS' is an eight letter word with none of the letters repeating.

Any 8-letter word with none of its letters repeating can be rearranged in 8! ways.

However, the question states that 'P' and 'S' should occupy the first and last position respectively.

Therefore, the first and last position can be filled in only one way.

The remaining 6 positions in between P and S can be filled with 6 other letters in in 6! ways.

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