Answer
a) $1.68\times10^{-6}$
b) $5.13\times10^{-7}$
c) $1.91\times10^{-7}$
d) $8.15\times10^{-8}$
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 $\frac{\binom{6}{6}\binom{24}{0}}{\binom{30}{6}}=\frac{1}{\binom{30}{6}}=1.68\times10^{-6}$
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 $\frac{\binom{6}{6}\binom{30}{0}}{\binom{36}{6}}=\frac{1}{\binom{36}{6}}=5.13\times10^{-7}$
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 $\frac{\binom{6}{6}\binom{36}{0}}{\binom{42}{6}}=\frac{1}{\binom{42}{6}}=1.91\times10^{-7}$
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 $\frac{\binom{6}{6}\binom{42}{0}}{\binom{48}{6}}=\frac{1}{\binom{48}{6}}=8.15\times10^{-8}$
