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There is money to send four of nine city council members to a conference in Honolulu. All want to go, so they decide to choose the members to go to the conference by a random process. How many different combinations of four council members can be selected from the nine who want to go to the conference

Sagot :

Answer:

126

Step-by-step explanation:

There are 9 city council members.

We have to choose 4 of them.

We have to use the combination as :

[tex]$^9C_4$[/tex]

where, 9 is the population size

4 is the sample size.

Therefore, the total number of possible samples without replacement is given as :

[tex]$^9C_4=\frac{9!}{4!(9-4)!}$[/tex]

      [tex]$=\frac{9!}{5! \ 4!}$[/tex]

     [tex]$=\frac{9 \times 8 \times 7 \times 6}{4 \times 3 \times 2 \times 1}$[/tex]

    = 126

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