Three numbers are chosen from 1 to 20. Find the probability that … - Vidyadip

Question

Three numbers are chosen from 1 to 20. Find the probability that they are consecutive.

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Answer

S = There numbers are chosen from 1 to 20
$n(S) = {^{20}C_3}$
$E =$ Group of three consecutive numbers between 1 and 20
$n(E) = 18$
$\{(1, 2, 3,), (2, 3, 4), (3, 4, 5), (4, 5, 6), (5, 6, 7), (6, 7, 8), (7, 8, 9), (8, 9, 10), (9, 10, 11), (10, 11, 12), (11, 12, 13), (11, 12, 13), (12, 13, 14), (13, 14, 15), (14, 15, 16), (15, 16, 17), (16, 17, 18), (17, 18, 19), (18, 19, 20)\}$
$\text{P(E)}=\frac{\text{n(E)}}{\text{n(S)}}$
$=\frac{18}{^{20}\text{C}_3}$
Required probability $=\frac{18}{^{20}\text{C}_3}$

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