Question

Three numbers are chosen at random from numbers 1 to 20. The probability that they are consecutive is

• A. (\frac{1}{190})
• B. (\frac{1}{120})
• C. (\frac{3}{190})
• D. [suspicious link removed]

Hint:

For (n) numbers, the number of consecutive sets of size (k) is (n - k + 1).

Answer 1

The Correct Option is C

Step 1: Total Outcomes
Total ways to choose 3 numbers from 20 = (^{20}C_3 = \frac{20 \times 19 \times 18}{3 \times 2 \times 1} = 20 \times 19 \times 3 = 1140).

Step 2: Favorable Outcomes
Consecutive sets: ((1,2,3), (2,3,4), \dots, (18,19,20)).
Total favorable sets = 18.

Step 3: Calculate Probability
P(Consecutive) = (\frac{18}{1140} = \frac{9}{570} = \frac{3}{190}).
Final Answer: (C)