From 6 programmers and 4 typists, an office wants to recruit 5 people. What is the number of ways this can be done so as to recruit at least one typist?

Step-by-step solution

Number of ways ^4 C ₁ ^6 C ₄+ ^4 C ₂ ^6 C ₃+ ^4 C ₃ ^6 C ₂+ ^4 C ₄ ^6 C ₁ aligned & =(4)(15)+(6)(20)+(4)(15)+(1)(6) & =60+120+60+6 & =246 aligned