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Sagot :
Answer:
Probability that all 4 memebers are administrators = 1/12972
Explanation:Number of administrators = 6
Number of teachers = 38
Number of staff = 4
Total number of employees in the school = 6 + 38 + 4
Total number of employees in the school = 48
Probability = (Number of possible outcomes) / (Number of total outcomes)
The number of total outcomes is the number of ways of selecting 4 committee members from 48 employess
Number of total outcomes = 48C4
[tex]\begin{gathered} \text{Number of total outcomes = }\frac{48!}{(48-4)!4!} \\ \text{Number of total outcomes = }\frac{48!}{44!4!} \\ \text{Number of total outcomes = }\frac{48\times47\times46\times45\times44!}{44!4\times3\times2\times1} \\ \text{Number }of\text{ total outcomes = 2}\times47\times46\times45 \\ \text{Number of total outcomes = 19458}0 \end{gathered}[/tex]Number of possible outcomes is the number of ways of selecting 4 committe memebers from 6 administrators
[tex]\begin{gathered} \text{Number of possible outcomes = 6C4} \\ \text{Number of possible outcomes = }\frac{6!}{(6-4)!4!} \\ \text{Number of possible outcomes = }\frac{6!}{2!4!} \\ \text{NUmber of ossible outcomes = }\frac{6\times5\times4!}{2\times1\times4!} \\ \text{Number of possible outcomes = 3 }\times\text{ 5} \\ \text{Number of possible outcomes = 15} \end{gathered}[/tex]Probability that all 4 memebers are administrators = 15/194580
Probability that all 4 memebers are administrators = 1/12972
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