Answer:
The probability that Teesha will not be picked as a guide is 88.5%.
Step-by-step explanation:
Given : Teesha is in the French club. There are 26 students in the club. The French teacher will pick 3 students at random to guide visiting students from France.
To find : What is the probability that Teesha will not be picked as a guide?
Solution :
First we find that the number of combinations we have with 26 students and picking 3:
[tex]^{26}C_3=\frac{26!}{3!\times 23!}[/tex]
[tex]^{26}C_3=\frac{26\times 25\times 24\times 23!}{3\times 2\times 23!}[/tex]
[tex]^{26}C_3=\frac{26\times 25\times 24}{3\times 2}[/tex]
[tex]^{26}C_3=2600[/tex]
Now, we have to find the number of ways when Teesha will not be picked as a guide.
The number of candidates reduced into 25.
[tex]^{25}C_3=\frac{25!}{3!\times 22!}[/tex]
[tex]^{25}C_3=\frac{25\times 24\times 23\times 22!}{3\times 2\times 22!}[/tex]
[tex]^{26}C_3=\frac{25\times 24\times 23}{3\times 2}[/tex]
[tex]^{26}C_3=2300[/tex]
So the probability that she won't be picked is:
[tex]P=\frac{2300}{2600}[/tex]
[tex]P=\frac{23}{26}[/tex]
[tex]P=0.885[/tex]
[tex]P=88.5\%[/tex]
Therefore, The probability that Teesha will not be picked as a guide is 88.5%.
