Question

Vanessa, Samantha Hannah , and jordyn are al part of a 12 member volleyball team. Four members of the teamare randomly selected to fill the water for the day What is the probability that all four of them will bechosen

Answer 1

We have 12 members of the team. We can calculate how many combinations of 4 members we can choose as a a combination of 12 in 4, where order does not matter:

`\begin{gathered} C(n,r)=(n!)/(r!(n-r)!) \\ C(12,4)=(12!)/(4!8!)=(12\cdot11\cdot10\cdot9)/(4\cdot3\cdot2\cdot1)=(11880)/(24)=495 \end{gathered}`

Then, if we want to know the chances that an specific combination (there is only one possible combination that include Vanessa, Samantha, Hannah, and Jordyn) is picked between the 495 possible combinations, we have to calculate:

`P(V,S,H,J)=(1)/(495)\approx0.002`

Answer: the probability is P=1/495=0.002.