What is the probability that four S’s come consecutively in the word ‘MISSISSIPPI’
A. $\dfrac{4}{{165}}$
B.$\dfrac{{16}}{{165}}$
C.$\dfrac{{12}}{{165}}$
D.$\dfrac{5}{{165}}$
Last updated date: 27th Mar 2023
•
Total views: 306.3k
•
Views today: 8.84k
Answer
306.3k+ views
Hint: We 1st take count of all 11 letters and rearrange them in total number of outcomes and then take S’s as a single letter and then find the favorable outcomes.
Complete step-by-step answer:
Total number of letters in MISSISSIPPI = 11 letters (4 – S, 4 – I, 2 – P, 1 – M)
Total number of ways of arranging MISSISSIPPI $ = \dfrac{{11!}}{{\left( {4!} \right)\left( {4!} \right)\left( {2!} \right)}}$
Now we need all S to be together
So, if we consider SSSS as 1 block then the remaining number of letters will be MIIIPPI = 8 letters
Number of ways of such arrangement $ = \dfrac{{8!}}{{\left( {4!} \right)\left( {2!} \right)}} = \dfrac{{8!}}{{4! \times 2}}$
Probability that all 4 S’s are together $ = \dfrac{2}{1}$
=$ = \dfrac{{8!}}{{\left( {4!} \right) \times 2}} \times = \dfrac{{\left( {4!} \right)\left( {4!} \right)\left( {2!} \right)}}{{11!}}$
$ = \dfrac{{8!}}{{11 \times 10 \times 9 \times 8!}} \times 4!$
$ = \dfrac{{4 \times 3 \times 2 \times 1}}{{11 \times 10 \times 9}} = \dfrac{4}{{165}}$
Therefore the probability of all ‘S’ are together =$\dfrac{4}{{165}}$
The correct answer is option (A)
Note: To solve such a question we first see what is the probability that four S’s which come consecutively if all the letters of the word MISSISSIPPI are rearranged randomly.
Complete step-by-step answer:
Total number of letters in MISSISSIPPI = 11 letters (4 – S, 4 – I, 2 – P, 1 – M)
Total number of ways of arranging MISSISSIPPI $ = \dfrac{{11!}}{{\left( {4!} \right)\left( {4!} \right)\left( {2!} \right)}}$
Now we need all S to be together
So, if we consider SSSS as 1 block then the remaining number of letters will be MIIIPPI = 8 letters
Number of ways of such arrangement $ = \dfrac{{8!}}{{\left( {4!} \right)\left( {2!} \right)}} = \dfrac{{8!}}{{4! \times 2}}$
Probability that all 4 S’s are together $ = \dfrac{2}{1}$
=$ = \dfrac{{8!}}{{\left( {4!} \right) \times 2}} \times = \dfrac{{\left( {4!} \right)\left( {4!} \right)\left( {2!} \right)}}{{11!}}$
$ = \dfrac{{8!}}{{11 \times 10 \times 9 \times 8!}} \times 4!$
$ = \dfrac{{4 \times 3 \times 2 \times 1}}{{11 \times 10 \times 9}} = \dfrac{4}{{165}}$
Therefore the probability of all ‘S’ are together =$\dfrac{4}{{165}}$
The correct answer is option (A)
Note: To solve such a question we first see what is the probability that four S’s which come consecutively if all the letters of the word MISSISSIPPI are rearranged randomly.
Recently Updated Pages
If ab and c are unit vectors then left ab2 right+bc2+ca2 class 12 maths JEE_Main

A rod AB of length 4 units moves horizontally when class 11 maths JEE_Main

Evaluate the value of intlimits0pi cos 3xdx A 0 B 1 class 12 maths JEE_Main

Which of the following is correct 1 nleft S cup T right class 10 maths JEE_Main

What is the area of the triangle with vertices Aleft class 11 maths JEE_Main

KCN reacts readily to give a cyanide with A Ethyl alcohol class 12 chemistry JEE_Main

Trending doubts
What was the capital of Kanishka A Mathura B Purushapura class 7 social studies CBSE

Difference Between Plant Cell and Animal Cell

Write an application to the principal requesting five class 10 english CBSE

Ray optics is valid when characteristic dimensions class 12 physics CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Tropic of Cancer passes through how many states? Name them.

Write the 6 fundamental rights of India and explain in detail

Write a letter to the principal requesting him to grant class 10 english CBSE

Name the Largest and the Smallest Cell in the Human Body ?
