Coelhothales wrote:
Whats the probability on having two consecutives letters C on word CLASSIC
P = (good arrangements)/(all possible arrangements).
All possible arrangements:
There are 7 letters in the word CLASSIC.
The number of ways to arrange 7 distinct elements = 7!.
But CLASSIC is not composed of 7 distinct letters: there are two identical C's and two identical S's.
When an arrangement includes identical elements, we must divide by the number ways each set of identical elements can be arranged.
The reason:
When the identical elements swap positions, the arrangement doesn't change.
Here, we must divide by 2! to account for the two identical C's and by another 2! to account for the two identical S's:
7!/(2!2!) = 7*6*5*3*2.
Good arrangements:
In a good arrangement, the two C's are in adjacent positions.
To ensure that the two C's are in adjacent positions, consider CC a single element in the arrangement.
Now count the number of ways to arrange the 6 elements CC, L, A, S, S, and I.
The number of ways to arrange 6 distinct elements = 6!.
To account for the two identical S's, divide by 2!:
6!/2! = 6*5*4*3.
P(the two C's are in adjacent positions) = (6*5*4*3)/(7*6*5*3*2) = 2/7.
Last edited by
GMATGuruNY on Thu Mar 27, 2014 5:35 pm, edited 1 time in total.
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