Multiple choice

Three integers are selected simultaneously from the set of integers {1,2,3,4,5,.......50}. The probability that the selected numbers are consecutive, is equal to

  1. $\displaystyle \frac{9}{(25)(49)}$
  2. $\displaystyle \frac{6}{(25)(49)}$
  3. $\displaystyle \frac{3}{(25)(49)}$
  4. $\displaystyle \frac{1}{25(49)}$
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C Correct answer
Explanation

The total number of ways to select 3 integers from 50 is 50C3 = (50 * 49 * 48) / 6. The number of favorable outcomes where the three integers are consecutive is 48 (from {1,2,3} to {48,49,50}). The probability is therefore 48 / 50C3 = 48 / (50 * 49 * 8) = 6 / (50 * 49) = 3 / (25 * 49).

AI explanation

The total number of ways to select 3 integers from a set of 50 is calculated using the combinations formula 50C3, which equals (50 * 49 * 48) / (3 * 2 * 1) or 19600. The number of ways to select three consecutive integers is 48, corresponding to the sets (1,2,3) through (48,49,50). The probability is therefore 48 / 19600, which simplifies by dividing the numerator and denominator by 16 to get 3 / (25 * 49).

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