Question

If the letters of the word regulations be arranged at random what is the probability that there will be exactly 4 letters between r and e

Answer 1

Answer:

Step-by-step explanation:

Given  

If the letters of the word regulations be arranged at random what is the probability that there will be exactly 4 letters between r and e

So the number of ways there are exactly 4 letters between R and E are

R is in first place so E will be in 6 th place

R is in second place so E will be in 7 th place

Similarly  

R is in 6th place so E will be in 11 th place.

R and E will interchange the positions and required number of favourable cases will be 2 x 6 = 12

There are 11 letters.

The positions are (1,6) (3,8)(2,7)(4,9)(5,10) and (6,11)

Remaining positions of other 9 letters can be arranged in 9! Ways. Total ways R and E have 4 letters between them = 6 x 2 x 9!

Now probability = 12 x 9! / 11! = 12 / 110 = 6/55

Answer 2

Answer:

12/110

Step-by-step explanation:

we know that,

here total 11 letters in this word, and we opt the letters 'r' & 'e'.

so total no. of the ways the letters r & e occupies =11p2 ways.

but we want to find the no of ways of exactly 4 letters between 'r '& 'e' .

we know that the positions for this condition are (r, e)=(1,6),(2,7),(3,8),(4,9),(5,10),(6,11) also (e, r)= (1,6),(2,7),(3,8),(4,9),(5,10),(6,11).

so total positions for exactly 4 lettets between 'r'&'e' are 6*2=12;

so probablity for exactly 4 letters b/w 'r'& 'e'= 12/110.