Answer:
[tex]Probability =0.1744[/tex]
Step-by-step explanation:
Given
Total
[tex]American = 11[/tex]
[tex]Canadian = 18[/tex]
Selection
[tex]American = 0[/tex]
[tex]Canadian = 4[/tex]
Required
Determine the probability of selecting a 4 committee member that are Canadian.
First, we calculate total possible selection.
[tex]Total = American + Canadian[/tex]
[tex]Total = 11 + 18[/tex]
[tex]Total = 27[/tex]
Number of ways to select 4 from 27 is:
[tex]^{27}C_4 = \frac{27!}{(27-4)!4!}[/tex]
[tex]^{27}C_4 = \frac{27!}{23!4!}[/tex]
[tex]^{27}C_4 = \frac{27*26*25*24*23!}{23!4!}[/tex]
[tex]^{27}C_4 = \frac{27*26*25*24}{4!}[/tex]
[tex]^{27}C_4 = \frac{27*26*25*24}{4*3*2*1}[/tex]
[tex]^{27}C_4 = \frac{421200}{24}[/tex]
[tex]^{27}C_4 = 17550[/tex]
Next, we calculate ways of selecting 4 Canadians from 18 is:
[tex]^{18}C_4 = \frac{18!}{(18-4)!4!}[/tex]
[tex]^{18}C_4 = \frac{18!}{14!4!}[/tex]
[tex]^{18}C_4 = \frac{18*17*16*15*14!}{14!4!}[/tex]
[tex]^{18}C_4 = \frac{18*17*16*15}{4!}[/tex]
[tex]^{18}C_4 = \frac{18*17*16*15}{4*3*2*1}[/tex]
[tex]^{18}C_4 = \frac{73440}{24}[/tex]
[tex]^{18}C_4 = 3060[/tex]
The required probability is:
[tex]Probability =\frac{3060}{17550}[/tex]
[tex]Probability =0.1744[/tex]
