# Answer to Question #2222 in Statistics and Probability for Shubham Agarwal

Question #2222

8 men in a company of 25 are graduate. If 3 mens are picked out of the 25 at random. What is the probability that at best 1 graduate?

Expert's answer

There are (25-8) = 17 ungraduated persons. The probability that at best 1 is graduate:

<img src="/cgi-bin/mimetex.cgi?P%28x%20%5Cleq%201%29%20=%20%5Cfrac%7B17%20%5Ccdot%2016%20%5Ccdot%2015%20%7D%7B25%20%5Ccdot%2024%20%5Ccdot%2023%7D%20+%203%20%5Cfrac%7B8%20%5Ccdot17%20%5Ccdot%2016%20%7D%7B25%20%5Ccdot%2024%20%5Ccdot%2023%7D%20=%200.7687" title="P(x \leq 1) = \frac{17 \cdot 16 \cdot 15 }{25 \cdot 24 \cdot 23} + 3 \frac{8 \cdot17 \cdot 16 }{25 \cdot 24 \cdot 23} = 0.7687">

<img src="/cgi-bin/mimetex.cgi?P%28x%20%5Cleq%201%29%20=%20%5Cfrac%7B17%20%5Ccdot%2016%20%5Ccdot%2015%20%7D%7B25%20%5Ccdot%2024%20%5Ccdot%2023%7D%20+%203%20%5Cfrac%7B8%20%5Ccdot17%20%5Ccdot%2016%20%7D%7B25%20%5Ccdot%2024%20%5Ccdot%2023%7D%20=%200.7687" title="P(x \leq 1) = \frac{17 \cdot 16 \cdot 15 }{25 \cdot 24 \cdot 23} + 3 \frac{8 \cdot17 \cdot 16 }{25 \cdot 24 \cdot 23} = 0.7687">

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