1. A group of 15 undergraduate and 15 graduate students are in a room. If 10 of the 30 students are selected at random and called sequentially by the instructor (order matters), what is the probability that all 10 are graduate students or all 10 are undergraduate students? 2. Select uniformly at random a permutation of {1,2, ..., 100}. What is the probability that in the selected permutation all numbers are in ascending order? 3. A group of 40 women and 40 men are in a room. A committee of 15 is chosen at random. Find the probability that the committee consists only of women.

A First Course in Probability (10th Edition)
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Chapter1: Combinatorial Analysis
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1. A group of 15 undergraduate and 15 graduate students are in a room. If 10 of the 30 students are
selected at random and called sequentially by the instructor (order matters), what is the probability
that all 10 are graduate students or all 10 are undergraduate students?
2. Select uniformly at random a permutation of {1,2, ..., 100}. What is the probability that in the selected
permutation all numbers are in ascending order?
3. A group of 40 women and 40 men are in a room. A committee of 15 is chosen at random. Find the
probability that the committee consists only of women.
Transcribed Image Text:1. A group of 15 undergraduate and 15 graduate students are in a room. If 10 of the 30 students are selected at random and called sequentially by the instructor (order matters), what is the probability that all 10 are graduate students or all 10 are undergraduate students? 2. Select uniformly at random a permutation of {1,2, ..., 100}. What is the probability that in the selected permutation all numbers are in ascending order? 3. A group of 40 women and 40 men are in a room. A committee of 15 is chosen at random. Find the probability that the committee consists only of women.
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