Answer
Verified
479.7k+ views
Hint: In order to solve this problem assume the 3 L as one letter then use the permutations and apply the formula of probability that number of favourable outcomes upon total number of outcomes and proceed it further. Doing this you will reach the right answer.
Complete step-by-step answer:
There are 1-H, 4-U and 3-L and hence total 8 alphabets.
Hence the total number of arrangements is 8!.
But there are 4 U and 3L so we will divide 8! with 3! and 4!.
So, the actual number of all arrangements =$\dfrac{{8!}}{{3!4!}}$
Taking all 3-L together, we should treat 3-L as one entity and hence total 6 distinct terms to be arranged. But the arrangement of 3-L =1 as all L are the same.
Now we have only 6 letters in which 4 letters are U.
So, number of arrangements with all 3-L together =$\dfrac{{6!}}{{4!}}$
Hence, the required probability = $\dfrac{{{\text{Number}}\,{\text{of}}\,{\text{favourable}}\,{\text{out}}\,{\text{comes}}}}{{{\text{total number of outcomes}}}}$
=$\dfrac{{\dfrac{{6!}}{{4!}}}}{{\dfrac{{8!}}{{3!4!}}}} = \dfrac{{6!}}{{4!}}{\text{x}}\dfrac{{4!3!}}{{8!}} = \dfrac{{6!{\text{x3!}}}}{{8!}} = \dfrac{{6!{\text{x3!}}}}{{6!{\text{x7x8}}}} = \dfrac{{3{\text{x2}}}}{{56}} = \dfrac{3}{{28}}$
Hence, the correct option is C.
Note: Whenever you face such type of problems you have to assume all the letters as one letter then solve using permutations and obtain the number of arrangements. Here we have asked to find the probability therefore we have obtained the total number of arrangements and the number of arrangements of the asked condition then we have applied the formula of probability. Using this will take you to the right answer.
Complete step-by-step answer:
There are 1-H, 4-U and 3-L and hence total 8 alphabets.
Hence the total number of arrangements is 8!.
But there are 4 U and 3L so we will divide 8! with 3! and 4!.
So, the actual number of all arrangements =$\dfrac{{8!}}{{3!4!}}$
Taking all 3-L together, we should treat 3-L as one entity and hence total 6 distinct terms to be arranged. But the arrangement of 3-L =1 as all L are the same.
Now we have only 6 letters in which 4 letters are U.
So, number of arrangements with all 3-L together =$\dfrac{{6!}}{{4!}}$
Hence, the required probability = $\dfrac{{{\text{Number}}\,{\text{of}}\,{\text{favourable}}\,{\text{out}}\,{\text{comes}}}}{{{\text{total number of outcomes}}}}$
=$\dfrac{{\dfrac{{6!}}{{4!}}}}{{\dfrac{{8!}}{{3!4!}}}} = \dfrac{{6!}}{{4!}}{\text{x}}\dfrac{{4!3!}}{{8!}} = \dfrac{{6!{\text{x3!}}}}{{8!}} = \dfrac{{6!{\text{x3!}}}}{{6!{\text{x7x8}}}} = \dfrac{{3{\text{x2}}}}{{56}} = \dfrac{3}{{28}}$
Hence, the correct option is C.
Note: Whenever you face such type of problems you have to assume all the letters as one letter then solve using permutations and obtain the number of arrangements. Here we have asked to find the probability therefore we have obtained the total number of arrangements and the number of arrangements of the asked condition then we have applied the formula of probability. Using this will take you to the right answer.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
Mark and label the given geoinformation on the outline class 11 social science CBSE
When people say No pun intended what does that mea class 8 english CBSE
Name the states which share their boundary with Indias class 9 social science CBSE
Give an account of the Northern Plains of India class 9 social science CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
In Indian rupees 1 trillion is equal to how many c class 8 maths CBSE
Which are the Top 10 Largest Countries of the World?
How do you graph the function fx 4x class 9 maths CBSE
Give 10 examples for herbs , shrubs , climbers , creepers
Difference Between Plant Cell and Animal Cell
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Why is there a time difference of about 5 hours between class 10 social science CBSE