A basket of fruits contains 5 bananas, 8 mangoes, and 7 apples. Two fruits are randomly selected without replacement. Calculate the probability of selecting an apple and a banana.
A. 3/5
B. 21/190
C. 7/76
D. 7/80
To calculate the probability of selecting an apple and a banana, we first need to calculate the total number of ways of selecting 2 fruits out of the total 20 fruits.
Total number of ways = 20 choose 2 = 20! / (2!(20-2)!) = 190
Next, we calculate the number of ways of selecting 1 apple out of 7 and 1 banana out of 5.
Number of ways = 7 choose 1 * 5 choose 1 = (7! / (1!(7-1)!)) * (5! / (1!(5-1)!)) = 7 * 5 = 35
Therefore, the probability of selecting an apple and a banana is the number of favorable outcomes (35) divided by the total number of ways (190).
Probability = 35/190 = 7/38
So, the correct answer is not among the given options.