Question

The first 8 alphabets are written down at random. what is the probability that the letters b,c,d,e always come together ?
A) 1/7
B) 8!
C) 7!
D) 1/14

Answer 1

Q:

The first 8 alphabets are written down at random. what is the probability that the letters b,c,d,e always come together ?

A) 1/7
B) 8!
C) 7!
D) 1/14

Answer:   D) 1/14 

Read Description:

8 letters can be written in 8! ways.

n(S) = 8!

Let E be the event that the letters b,c,d,e always come together when the first 8 alphabets are written down.

Now the letters a, (bcde), f, g and h can be arranged in 5! ways.

The letters b,c,d and e can be arranged themselves in 4! ways.

n(E) = 5! x 4!

Now, the required P(E) = n(E)/n(S) = 5! x 4!/8! = 1/14

Therefore, the answer is 1/14. 

Answer 2

The 8 letters can be written in 8! ways.
n(S) = 8!

Let E be the event that the letters b,c,d,e always come together when the first 8 alphabets are written down.

Now the letters a, (bcde), f, g and h can be arranged in 5! ways.

The letters b,c,d and e can be arranged themselves in 4! ways.

n(E) = 5! x 4!

Now, the required P(E) = n(E)/n(S) = 5! x 4!/8! = 1/14

Hence the answer is 1/14. 
✔✔