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The first 7 alphabets are written down at random. what is the probability that the letters a,b,c always come together?
- A1/7
- B2/7
- C3/7
- D4/7
Correct answer: A
Discussion 1
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CCommunity
1/7
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 the answer is 1/7.
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 the answer is 1/7.