Q170 / 270 · NDA 2019 (Phase 1) · Mathematics

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?

  • A
    209
  • B
    210
  • Correct answer
    C
    246
  • D
    242

Solution

Number of ways ${ }^4 \mathrm{C}_1{ }^6 \mathrm{C}_4+{ }^4 \mathrm{C}_2{ }^6 \mathrm{C}_3+{ }^4 \mathrm{C}_3{ }^6 \mathrm{C}_2+{ }^4 \mathrm{C}_4{ }^6 \mathrm{C}_1$ $\begin{aligned} & =(4)(15)+(6)(20)+(4)(15)+(1)(6) \\ & =60+120+60+6 \\ & =246\end{aligned}$

Hence, the correct answer is option: 'C'.

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