A 6 letter permutation is selected at random from the letters NIMBLE. What is the probability that:
a. the second letter is a vowel and the third is a consonant?
b.the second and third letters are both vowels?
c.the second letter is aconsonant and the last letter is E?
d. the second letter is a consonant and the last letter is L?
In the above images answers are given to parts a, b, c, and d of the problem, respectively. I have used probability trees to calculate the probability of each outcome. The paths leading to a given outcome are indicated in red. Probability of a path is calculated by multiplying the individual probabilities on the path. You add the path probabilities to find the probability of each outcome.