A probability problem by pulkit singh

Probability Level 2

The number of ways of arranging letters of HAVANA so that V and N do not appear together is


The answer is 80.

Pulkit Singh by pulkit singh , 21, India

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3 solutions

Aditya Desai
Dec 9, 2014

6!/3!---5!*2!/3!

2 Helpful 0 Interesting 0 Brilliant 0 Confused
Bk Lim
Dec 14, 2014

N is left out.

So we have 5!/3! = 20 to arrange HAVAA

Now insert N into 4 slots (both sides of H is not available)

20 x 4 =80

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Venture Hi
Dec 9, 2014

The number of ways we can arrange the word H-A-V-A-N-A is 6!/3! =120 ways. This total minus the number of ways to arrange HAVANA where V and N are together gives you the total of ways of arranging letters HAvANA so that V and N do not appear together.
Treat V-N ( N-V) as one letter. So, this leaves you with H-A-A-A. The total number of ways of arranging this 5 letters is 5!/3!=20. Since V-N and N-V have two configuration, we multiply 20 by 2= 400 ways. Thuis, 120-40 =80 ways.

1 Helpful 0 Interesting 0 Brilliant 0 Confused

missed a century as my first answer was 100

sakshi rathore - 5 years, 11 months ago

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