Question 1199022
.
A corporation has six male senior executives and four female senior
executives. Four senior executives are chosen at random to attend a
technology seminar. What is the probability of choosing
(a) four men?
(b) four women?
(c) two men and two women?
(d) one man and three women?
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Common information:  total number of persons = 6 + 4 = 10.


(a)  P = {{{C[6]^4/C[10]^4}}} = {{{15/210}}} = {{{1/14}}}.    <U>ANSWER</U>

     The denominator is the total number of all possible quadruples of 10 persons.

     The numerator is the number of all possible quadruples of 6 males.



(b)  P = {{{C[4]^4/C[10]^4}}} = {{{1/210}}}.          <U>ANSWER</U>

     The denominator is the total number of all possible quadruples of 10 persons.

     The numerator is the number of all possible quadruples of 4 females.



(c)  P = {{{C[6]^2*C[4]^2)/C[10]^4}}} = {{{(15*6)/210}}} = {{{90/210}}} = {{{3/7}}}.     <U>ANSWER</U>

     The denominator is the total number of all possible quadruples of 10 persons.

     The numerator is the number of all possible quadruples of 2 males and 2 females.
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Solved for all parts &nbsp;(a), &nbsp;(b) &nbsp;and &nbsp;(c), &nbsp;excluding &nbsp;(d).


I left &nbsp;(d) &nbsp;for you in order for &nbsp;YOU &nbsp;complete it on your own.