Permutations #3

Probability Level 1

The letters of the word TUESDAY are arranged in line, each arrangement ending with a letter S.

(a)How many different arrangements are possible?
(b)How many of them start with the letter D?

Write the solution as sum of solutions of (a) and (b).


The answer is 840.

A Former Brilliant Member by A Former Brilliant Member

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2 solutions

Siddharth Singh
Jul 16, 2015

There are 7 places to be filled.

(a). Since the last place should contain S only then 6 places are left so 6 places can be filled in 6! ways=720.

(b).Now first place is also occupied by D therefore we are left with 5 unfilled places which can be filled in 5! ways=120

(a)+(b)=720+120= 840 \boxed{840} .

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Usama Bin Saeed
Aug 6, 2015

Since "S" is fixed to the extreme right side therefore there is 6 possibilities for other 6 letters hence no: of ways will be 6!=720. In second condition "D" is also fixed to the extreme left side therefore there is 5 possibilities for other 5 letters hence no: of ways will be 5!=120. By adding no: of ways; 720+120=840 (Answer)

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