First class

The shipment contains 40 items. 36 are first-grade, and four are defective. How many ways can we select five items so that it is no more than one defective?

Correct answer:

n =  612612

Step-by-step explanation:

$$\begin{gathered} C_5(36)=\left(\genfrac{}{}{0ex}{}{36}{5}\right)=\frac{36!}{5!(36-5)!}=\frac{36\cdot 35\cdot 34\cdot 33\cdot 32}{5\cdot 4\cdot 3\cdot 2\cdot 1}=376992 \\ {n}_1=\left(\genfrac{}{}{0ex}{}{36}{5}\right)=376992 \\ {C}_4(36)=\left(\genfrac{}{}{0ex}{}{36}{4}\right)=\frac{36!}{4!(36-4)!}=\frac{36\cdot 35\cdot 34\cdot 33}{4\cdot 3\cdot 2\cdot 1}=58905 \\ {n}_2=4\cdot \left(\genfrac{}{}{0ex}{}{36}{4}\right)=4\cdot 58905=235620 \\ n=n_1+n_2=376992+235620=612612 \end{gathered}$$

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