Aclass has 14 boys and 6 girls.suppose three students are selected at random from the class.find the probability that they are all boys
14/20 * 13/19 * 12/18
mettu university
To find the probability that all three selected students are boys, we need to calculate the ratio of the number of favorable outcomes (3 boys selected) to the number of possible outcomes (any 3 students selected).
First, let's calculate the number of possible outcomes of selecting three students from a class of 20 (14 boys and 6 girls). We can do this using combinations.
The number of possible outcomes is given by the combination formula:
nCr = n! / (r!(n-r)!)
In this case, n = 20 (total number of students) and r = 3 (number of students we want to select).
So, the number of possible outcomes is:
20C3 = 20! / (3!(20-3)!) = (20 * 19 * 18) / (3 * 2 * 1) = 1140
Next, let's calculate the number of favorable outcomes, i.e., the number of ways to select 3 boys from a group of 14 boys.
This can be calculated in the same way:
14C3 = 14! / (3!(14-3)!) = (14 * 13 * 12) / (3 * 2 * 1) = 364
Now we can find the probability that all three selected students are boys:
Probability = Favorable outcomes / Possible outcomes = 364 / 1140 ≈ 0.319
Therefore, the probability that all three selected students are boys is approximately 0.319 or 31.9%.