Answer
a) 0.435
b) 0.416
c) 0.392
d) 0.367
Work Step by Step
a) Use binomial coefficients to compute the probability.
Choose 1 out of the 6 correct integers and choose 5 of the remaining 34 integers.
This can be done in $\frac{\binom{6}{1}\binom{34}{5}}{\binom{40}{6}}=0.435
$
b) Use binomial coefficients to compute the probability.
Choose 1 out of the 6 correct integers and choose 5 of the remaining 42 integers.
This can be done in $\frac{\binom{6}{1}\binom{42}{5}}{\binom{48}{6}}=0.416
$
c) Use binomial coefficients to compute the probability.
Choose 1 out of the 6 correct integers and choose 5 of the remaining 50 integers.
This can be done in $\frac{\binom{6}{1}\binom{50}{5}}{\binom{56}{6}}=0.4392
$
d) Use binomial coefficients to compute the probability.
Choose 1 out of the 6 correct integers and choose 5 of the remaining 58 integers.
This can be done in $\frac{\binom{6}{1}\binom{58}{5}}{\binom{64}{6}}=0.367
$
