Multiple choice

Directions: The question given below is followed by two statements I and II. You have to identify which statement(s) is/are sufficient to answer the question and mark the appropriate option. In how many ways can two different kinds of balls be picked from a bucket containing 15 balls? I. The bucket contains red and white balls in the ratio of 1 : 2. II. All the white balls are identical and none of the red balls is identical.

  1. Statement I alone is sufficient to answer the question.

  2. Statement II alone is sufficient to answer the question.

  3. Both the statements together are sufficient to answer the question.

  4. Both the statements together are insufficient to answer the question.

  5. Either of the statements alone is sufficient to answer the question.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Statement I gives the ratio of red to white balls (1:2), meaning 5 red and 10 white. Statement II says white are identical and red are not. To pick two different kinds of balls, we need one red and one white. Since white are identical, there is only 1 way to pick a white ball. Since red are not identical, there are 5 ways to pick a red ball. Total ways = 5 * 1 = 5. Both statements are needed.

AI explanation

Statement I gives the ratio of balls, meaning there are 5 red and 10 white balls out of the 15 total, but without statement II we assume standard combinations yielding 5C1 times 10C1 equals 50 ways. Statement II reveals the balls are not all identical, confirming we must use the distinct counts rather than simply choosing two groups. Together, they provide the exact types and quantities needed to calculate the number of ways, so both statements together are sufficient.

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