Question

The executive of an organization is to be selected from a group of 6 males and 7 females.

1. How many ways are there to choose the president and secretary?

2. How many ways are there to have a female president and a male secretary?

3. What is the probability that a randomly chosen president is female and a randomly chosen secretary is male?

4.  How many ways are there to choose a president, secretary and treasurer?

5. How many ways are there to choose a president, secretary and treasurer so that two are male and one is female?

6.  What is the probability that a randomly chosen president, secretary and treasurer include two males and one female?

Answer 1

1)

ways to choose president and secretary from 13 people =N(for first post 13 and for second 12 choices are there)=13*12=156

2)

ways to select  a female president and a male secretary =N(7 choice for president and 6 for seretary)

=7*6 =42

3)

P(president is female and a randomly chosen secretary is male)=42/156=7/26

4)

number of ways =13*12*11=1716

5)

number of ways =N(selecting 2 from 6 male and 1 female and then assign them in their posts)

= =15*7*6=630

6) hence probability =630/1716=105/286