Multiple choice

Andrew has a certain number of soccer balls with him. He wants to take two of the soccer balls for Match-1 on Monday and three of the soccer balls for Match-2 on Tuesday. There are exactly 15 ways in which he can select the soccer balls for Match-1, and all soccer balls can be used for both the matches. In how many different ways can Andrew select the soccer balls for Match-2?

  1. 20

  2. 15

  3. 10

  4. 9

  5. 8
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let n be the number of soccer balls. Selecting 2 balls in 15 ways means nC2 = 15. n(n-1)/2 = 15, so n(n-1) = 30, n = 6. Selecting 3 balls for the second match is 6C3 = (6*5*4)/(3*2*1) = 20.

AI explanation

Using the combinations formula nC2 = 15 to find the total number of soccer balls, we solve n(n-1)/2 = 15 to get n = 6. To find the ways to choose three balls for Match-2, we calculate 6C3. The result is (6 * 5 * 4) / (3 * 2 * 1), which equals 20 ways.

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