Acomittee of c people is chosen from a group consisting of m males and f females. what is the probability that mary and peter will not be serving together?
the probability that Mary and Peter will not be serving together:
probability that Mary is in a committee and Peter is not in a committee +
probability that Peter is in a committee and Mary is not in a committee +
probability that Peter and Mary both are not in a committee
probability that Mary is in a committee and Peter is not in a committee:
"P_1=1\/C^{c-1}_{m+f-1}=\\frac{(c-1)!(m+f-c)!}{(m+f-1)!}"
probability that Mary is in a committee and Peter is not in a committee:
"P_2=P_1=1\/C^{c-1}_{m+f-2}=\\frac{(c-1)!(m+f-c)!}{(m+f-1)!}"
probability that Peter and Mary both are not in a committee:
"P_3=1\/C^{c}_{m+f-2}=\\frac{c!(m+f-c-2)!}{(m+f-2)!}"
Answer:
"P=P_1+P_2+P_3=\\frac{2(c-1)!(m+f-c)!}{(m+f-1)!}+\\frac{c!(m+f-c-2)!}{(m+f-2)!}"
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