Question

An employee group requires 7 people be chosen for a committee from a group of 16 employees. Determine the following probabilities of randomly drawn committee of 7 employees. Write your answers as percents rounded to 4 decimal places. The employee group has 6 women and 10 men. What is the probability that 3 of the people chosen for the committee are women and 4 people chosen for the committee are men? % The committee requires that exactly 3 people from Customer Service serve on the committee. There are 5 people in Customer Service. What is the probability that exactly 3 of the people chosen for the committee are from Customer Service? % A bag contains 7 red marbles, 6 white marbles, and 5 blue marbles. You draw 4 marbles out at random, without replacement. Find each probability. P( all 4 are red )= A poker hand consists of five cards randomly dealt from a standard deck of 52 cards. The order of the cards does not matter. Determine the following probabilities for a 5-card poker hand. Write your answers in percent form, rounded to 4 decimal places. Determine the probability that exactly 4 of these cards are Aces. Answer: of ___% Determine the probability that all five of these cards are Spades. Answer: 08% Determine the probability that exactly 4 of these cards are face cards. Answer: ____% Determine the probability of selecting exactly 2 Aces and exactly 2 Kings Answer: ___% Determine the probability of selecting exactly 1 Jack. Answer: ___%

Answer 1

`1.)\\\frac{{6\choose3}*{10\choose4}}{{16\choose7}}= 36.7133\\2.)\\\frac{{5\choose3}*{11\choose4}}{{16\choose7}}= 28.8462\\3.)\\\frac{{7\choose4}}{{18\choose4}}= 1.1438\\4.)\\\frac{{4\choose4}*{48\choose1}}{{52\choose5}}= .0018\\5.)\\\frac{{13\choose5}}{{52\choose5}} = .0495\\6.)\\\frac{{12\choose4}*{40\choose1}}{{52\choose5}}= .7618\\7.)\\\frac{{4\choose2}*{4\choose2}*{44\choose1}}{{52\choose5}}= .0609\\8.)\\\frac{{4\choose1}*{48\choose4}}{{52\choose5}}= .2995`

all numbers were intended to % attached at the end, i just don't know how to do it.