Four numbers are chosen at random from $\{1,2,3, \ldots, 40\}$. The probability that they are not…
Four numbers are chosen at random from $\{1,2,3, \ldots, 40\}$. The probability that they are not consecutive, is
$\frac{1}{2470}$
$\frac{4}{7969}$
$\frac{2469}{2470}$
$\frac{7965}{7969}$
Solution
Probability that four of the numbers are consecutive
$=\frac{{ }^{37} C_1}{{ }^{40} C_4}$
Now, probability that four of the numbers are
Now, probability that four of the numbers are
consecutive $=1-\frac{{ }^{37} C_1}{{ }^{40} C_4}$
$=\frac{2469}{2470}$