Explanation:

The 7 letters can be written in 7! ways.
n(S) = 7!
Let E be the event that the letters a,b,c always come together when the first 7 alphabets are written down.
Now the letters (abc), d, e, f and g can be arranged in 5! ways.
The letters a,b and c can be arranged themselves in 3! ways.
n(E) = 5! x 3!
Now, the required P(E) = n(E)/n(S) = 5! x 3!/7! = 1/7

Hence, option 1 is the correct answer.