A president, vice-president, secretary, and treasurer can be chosen from a club with 9 members in 3024 ways
Further explanation
The probability of an event is defined as the possibility of an event occurring against sample space.
[tex]\large { \boxed {P(A) = \frac{\text{Number of Favorable Outcomes to A}}{\text {Total Number of Outcomes}} } }[/tex]
Permutation ( Arrangement )
Permutation is the number of ways to arrange objects.
[tex]\large {\boxed {^nP_r = \frac{n!}{(n - r)!} } }[/tex]
Combination ( Selection )
Combination is the number of ways to select objects.
[tex]\large {\boxed {^nC_r = \frac{n!}{r! (n - r)!} } }[/tex]
Let us tackle the problem!
There are 9 members in a club.
We will arrange 4 of the club members to be a president, vice-president, secretary, and treasurer.
In this problem we use the permutation formula as follows.
[tex]^nP_r = \frac{n!}{(n - r)!}[/tex]
[tex]^9P_4 = \frac{9!}{(9 - 4)!}[/tex]
[tex]^9P_4 = \frac{9!}{5!}[/tex]
[tex]^9P_4 = 6 \time 7 \times 8 \times 9[/tex]
[tex]^9P_4 = 3024[/tex]
Learn more
- Visit The Cities : https://brainly.com/question/8908016
- Rolling a six-sided die : https://brainly.com/question/1637111
- Combined Probability of Two Events : https://brainly.com/question/12745908
- Different Birthdays : brainly.com/question/7567074
Answer details
Grade: High School
Subject: Mathematics
Chapter: Probability
Keywords: Probability , Permutation , Combination , Alphabetical , Order , Arrangement , Selection
