Three balls are drawn randomly from a box containing balls with the twenty-six letters of the alphabet on them. Determine the probability of selecting C and F.
There are 26 balls in total, so the probability of selecting C as the first ball is 1/26.
After selecting the first ball, there are 25 remaining balls in the box, so the probability of selecting F as the second ball is 1/25.
Finally, after selecting the first two balls, there are 24 remaining balls in the box, so the probability of selecting any ball as the third ball is 1/24.
So the probability of selecting C and F is (1/26) * (1/25) * (1/24) = 1/15,600.
To determine the probability of selecting C and F, we need to consider the total number of possible outcomes and the number of favorable outcomes.
Total number of outcomes:
Since there are 26 letters in the alphabet, there are 26 balls in the box. When we draw three balls randomly, the total number of possible outcomes will be calculated using combinations.
The number of combinations of 26 letters taken 3 at a time can be calculated as:
C(26, 3) = (26!)/(3!(26-3)!) = 2600
Number of favorable outcomes:
To select C and F, we need to choose them out of the 26 letters and choose the remaining one letter from the remaining 24 letters.
The number of combinations of 2 letters chosen from C and F can be calculated as:
C(2, 2) = (2!)/(2!(2-2)!) = 1
The number of combinations of 1 letter chosen from the remaining 24 letters can be calculated as:
C(24, 1) = (24!)/(1!(24-1)!) = 24
Therefore, the total number of favorable outcomes is:
1 (for C and F together) multiplied by 24 (for choosing the remaining letter) = 24
Probability of selecting C and F:
Probability = (Number of favorable outcomes) / (Total number of outcomes)
Probability = 24 / 2600
Probability = 0.0092 (rounded to four decimal places)
Therefore, the probability of selecting C and F is approximately 0.0092.