Question 25 of 42intermediate🔧 ApplyNumerical3 marks

Find the number of ways of selecting 9 balls from 6 red balls, 5 white balls and 5 blue balls if each selection consists of 3 balls of each colour.

Correct Answer

2000 ways

Exercise: EXERCISE 6.4 | Q: 5 | (Chapter: 20)
For More Understanding

Explanation

This is a combination problem where we need to select 3 balls of each colour from the available balls. Since the selections of different colours are independent events, we apply the multiplication principle of counting. We calculate the combinations separately for each colour and multiply them together.

Solution Steps

  1. Step 1: Identify the selections required - We need to select 3 red balls from 6 red balls, 3 white balls from 5 white balls, and 3 blue balls from 5 blue balls.

  2. Step 2: Calculate ways for each colour - Number of ways to select 3 red balls from 6 = ⁶C₃ = 6!/(3! × 3!) = (6×56 \times 5 × 4)/(3×23 \times 2 × 1) = 20 ways.

  3. Step 3: Calculate ways for white balls - Number of ways to select 3 white balls from 5 = ⁵C₃ = 5!/(3! × 2!) = (5×45 \times 4)/2 = 10 ways.

  4. Step 4: Calculate ways for blue balls - Number of ways to select 3 blue balls from 5 = ⁵C₃ = 5!/(3! × 2!) = (5×45 \times 4)/2 = 10 ways.

  5. Step 5: Apply multiplication principle - Total number of ways = ⁶C₃ × ⁵C₃ × ⁵C₃ = 20×1020 \times 10 × 10 = 2000 ways.

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