Of the 5 distinguishable wires that lead into an apartment, 2 are for cable television service, and 3 are for telephone service. Using these wires, how many distinct combinations of 3 wires are there such that at least 1 of the wires is for cable television?  Choose the correct answer
A) 6  B) 7  C) 8  D) 9  E) 10
In these Q, where at least is used, the best is to find none and then subtract from total..   here total ways= 5C3=5!/3!2!=10..   ways where no cable television is used=3c3=1..   therefore ways containing at least one wire of cable tele=10-1=9..   Ans: 9
<result>D</result>
Of the 5 distinguishable wires that lead into an apartment, 2 are for cable television service, and 3 are for telephone service. Using these wires, how many distinct combinations of 3 wires are there such that at least 1 of the wires is for cable television?