Suppose a college application asks students to choose, in order, 3 of the following words that best describe them: leader, innovative, determined, logical, empathetic, dreamer, analytical. A college admission officer is lazy and decides to admit any student that chooses innovative and analytical as two of the three as long as innovative is before analytical, OR if they choose empathetic and innovative (in any order).

a. Supposing that applicants are equally likely to choose any 3 of the 7 words, what is the probability that a student will be admitted by this admission officer?

b. What is the probability that in the first 10 applications the officer reads, exactly 4 students are admitted.