Advertisement Remove all ads

If the Letters of the Word 'Mississippi' Are Written Down at Random in a Row, What is the Probability that Four S'S Come Together. - Mathematics

If the letters of the word 'MISSISSIPPI' are written down at random in a row, what is the probability that four S's come together.

 
Advertisement Remove all ads

Solution

There are 11 letters in the word ‘MISSISSIPPI’ which can be arranged in 11! ways.
Number of the letter S = 4
Let us consider the four S's  in the given word as one letter.
So, when the four letters are clubbed together, we have (SSSS) MIIIPPI. We can arrange eight letters in a row in 8! ways.
Also, the four S's can be arranges in 4! ways.
Hence, required probability = \[\frac{8! \times 4!}{11!} = \frac{8! \times 4 \times 3 \times 2}{11 \times 10 \times 9 \times 8!} = \frac{4 \times 3 \times 2}{11 \times 10 \times 9} = \frac{4}{165}\]

 

  Is there an error in this question or solution?
Advertisement Remove all ads

APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 33 Probability
Q 6 | Page 71
Advertisement Remove all ads

Video TutorialsVIEW ALL [1]

Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×