How many ways can a committee consisting of 3 members be formed from 9 people? ...

Questions

marychrisbalunan565 @marychrisbalunan565

October 2022 1 1 Report

How many ways can a committee consisting of 3 members be formed from 9
people?
Use the formula: C(n, r) =
n!
r! (n − r)!

where n = 9 and r = 3
NEED KO NA PLS

Answers & Comments

JuliaSlodava

‹PERMUTATIONS›

$\tt\color{skyblue}{\overline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}}$

$\large\rm{❛PROBLEM❜}$

How many ways can a committee consisting of 3 members be formed from 9 people?

$\tt\color{skyblue}{\overline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}}$

$\large\rm{❛ANSWER❜}$

$\large\bold{84 \: ways}$

$\tt\color{skyblue}{\overline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}}$

$\large\rm{❛GIVEN❜}$

$\small\bold{N \: = \: 9}$

$\small\bold{R \: = \: 3}$

$\tt\color{skyblue}{\overline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}}$

$\large\rm{❛FORMULA❜}$

↳ To determine how many ways of committies can be formed, here's the formula that we could use.

$\small\rm{_nC_r \: = \: \frac{n!}{[r! \: (n - r)!]}} \\$

$\tt\color{skyblue}{\overline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}}$

$\large\rm{❛SOLUTION❜}$

↳ Since, committee consists of 3 members from 9 people, so we'll need to write the equation as.

$\small\rm{_nC_r \: = \: \frac{n!}{[r! \: (n - r)!]}} \\$

↳ Substitute the given value to determine how many committies can be formed.

$\small\rm{_9C_3 \: = \: \frac{9!}{[3! \: (9 - 3)!]}} \\$

↳ Subtract the group of members in 9 people.

$\small\rm{_9C_3 \: = \: \frac{9!}{3! \: 6!}} \\$

↳ Multiply 9-1 and 6-1, then cancel out the number with similar value.

$\small\rm{_9C_3 \: = \: \frac{9! \: • \: 8! \: • \: 7! \: • \: \cancel6! \: • \: \cancel5! \: • \: \cancel4! \: • \: \cancel3! \: • \: \cancel2!}{3! \: • \: 2! \: \: \: \: \: \: \cancel6! \: • \: \cancel5! \: • \: \cancel4! \: • \: \cancel3! \: • \: \cancel2!}} \\$