First class

The shipment contains 40 items. 36 are first grade, 4 are defective. How many ways can select 5 items, so that it is no more than one defective?

Correct answer:

n =  612612

Step-by-step explanation:

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

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