Answer
a) $1.68×10^{−6}
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b) $5.13×10^{−7}
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c) $1.91×10^{−7}
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d) $8.15×10^{−8}
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Work Step by Step
a) Use binomial coefficients to compute the probability.
Choose 6 out of the 6 correct integers and none of the remaining 24 integers.
This can be done in $\frac{\binom{6}{6}\binom{24}{6}}{\binom{30}{6}}=\frac{1}{\binom{30}{6}}=1.68×10^{−6}
$
b) Use binomial coefficients to compute the probability.
Choose 6 out of the 6 correct integers and none of the remaining 30 integers.
This can be done in $\frac{\binom{6}{6}\binom{30}{6}}{\binom{36}{6}}=\frac{1}{\binom{36}{6}}=5.13×10^{−7}
$
c) Use binomial coefficients to compute the probability.
Choose 6 out of the 6 correct integers and none of the remaining 36 integers.
This can be done in $\frac{\binom{6}{6}\binom{36}{6}}{\binom{42}{6}}=\frac{1}{\binom{42}{6}}=1.91×10^{−7}
$
d) Use binomial coefficients to compute the probability.
Choose 6 out of the 6 correct integers and none of the remaining 42 integers.
This can be done in $\frac{\binom{6}{6}\binom{42}{6}}{\binom{48}{6}}=\frac{1}{\binom{48}{6}}=8.15×10^{−8}
$
