Five men in a company of $20$ are graduates. If $3$ men are picked out at random. The probability that at least one is a graduate is

\frac{^{15} C_{3}}{^{20} C_{3}}

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\frac{^{5} C_{3}}{^{20} C_{3}}

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1 - \frac{^{15} C_{3}}{^{20} C_{3}}

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1 - \frac{^{5} C_{3}}{^{20} C_{3}}

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Solution

The correct option is C $1 - \frac{^{15} C_{3}}{^{20} C_{3}}$
The probability that at least one is a graduate $= 1 -$ probability that no one of them is a graduate
$= 1 -^{15} C_{3} /^{20} C_{3}$

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Similar questions

1 \cdot^{20} C_{1} - 2 \cdot^{20} C_{2} + 3 \cdot^{20} C_{3} - \dots - 20 \cdot^{20} C_{20}

20_{1}^{C} - 2 \times 20_{2}^{C} + 3 \times 20_{3}^{C}

20 \times 20_{2}^{C} 0

^{20} C_{0} -^{20} C_{1} +^{20} C_{2} -^{20} C_{3} + - . . +^{20} C_{10}

{\frac{1}{2}}^{20} C_{10}

^{10} C_{3} +^{11} C_{3} +^{12} C_{3} + . . . . +^{20} C_{3}

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