Answer to Question #308779 in Statistics and Probability for brhy

Question

1.  How many ways can you pick a president, vice-president, and secretary from a group of six boys and five girls if 

a) there are no restrictions?

b) there must be at least one boy chosen?

c) there must be only one girl chosen?

Answer 1

Solution

a.      No restriction

n=11,    r=3

_nP_r= n!/(n-r)!

=11!/(11-3)!

=990 ways

b.      At least on boy chosen

₁₁P₃ - ₅P₃

=11!/(11-3)! – 5!/(5-3)!

= 990 – 60

= 930 ways

c.      Only one girl chosen

₅P₁ * ₆P₂ * 3

=5!/(5-1)! * 6!/(6-2)! * 3

=450 ways