Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 11
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The Letters of the Word 'Fortunates' Are Arranged at Random in a Row. What is the Chance that the Two 'T' Come Together. - Mathematics

The letters of the word 'FORTUNATES' are arranged at random in a row. What is the chance that the two 'T' come together.

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Solution

There are 10 letters in the word ‘FORTUNATES’, which can be arranged in 10! ways.
There are two T's in the word.
Let us consider these two letters in the word ‘FORTUNATES’ as one letter.
So, when the two T's are clubbed together, we have (T,T) FORUNAES.
We can arrange 9 letters in a row in 9! ways.
Also, the two T's can themselves be arranged in 2! ways.
Hence, required probability = \[\frac{9! \times 2!}{10!} = \frac{9! \times 2}{10 \times 9!} = \frac{1}{5}\]

 

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APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 33 Probability
Exercise 33.3 | Q 23 | Page 47
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