Find the number of ways of selecting 9 balls from 6 red balls , 5 white balls and 5 blue balls if each selection consist of 3 balls of each other ?

Question

Answer

Number of red balls=6,
number of white balls=5,
number of blue Balls=5,
number of ways of selecting 3 red balls=6C3,
=6!/3!3!=1×2×3×4×5×6/1×2×3×1×2×3=20,
number of ways of selecting 3 white balls=5C3,
=5!/3!2!=1×2×3×4×5×6/1×2×3×1×2=10,
number of ways of selecting 3 blue balls=5C3=
10,
total number of ways=20.10.10=2000 ways

Answer

Total number of red balls = 6
total number of white balls = 5
total number of blue balls = 5
now,
3 red balls out of 6 red balls can be selected in ⁶C₃ ways .

3 white balls out of 5 white balls can be selected in ⁵C₃ ways .

3 blue balls out of 5 blue balls can be selected in ⁵C₃ ways .

now, A/C to fundamental principal of counting,
total number of ways selecting 9 balls (3 balls of each colors ) is
= ⁶C₃ × ⁵C₃ × ⁵C₃
= 6!/3!×3! × 5!/3!×2! × 5!/3!×2!
= (6 × 5 × 4/6 ) × ( 5 × 4/2) × (5 × 4/2)
= 20 × 10 × 10
= 2000 ways .

Answer

6C3+5C3+5C3

Answer

**Introduction:**
In this problem, we are given 6 red balls, 5 white balls, and 5 blue balls. We need to find the number of ways to select 9 balls such that each selection consists of 3 balls of each color.

**Approach:**
To solve this problem, we can use the concept of combinations. We need to select 3 red balls, 3 white balls, and 3 blue balls from their respective groups.

**Step 1: Selecting red balls**
We have 6 red balls, and we need to select 3 of them. The number of ways to do this is given by the combination formula:

C(6, 3) = 6! / (3! * (6-3)!) = 20

**Step 2: Selecting white balls**
We have 5 white balls, and we need to select 3 of them. The number of ways to do this is also given by the combination formula:

C(5, 3) = 5! / (3! * (5-3)!) = 10

**Step 3: Selecting blue balls**
Similarly, we have 5 blue balls, and we need to select 3 of them. The number of ways to do this is given by the combination formula:

C(5, 3) = 5! / (3! * (5-3)!) = 10

**Step 4: Total number of ways**
To find the total number of ways to select 9 balls, we need to multiply the number of ways from each step:

Total number of ways = Number of ways to select red balls * Number of ways to select white balls * Number of ways to select blue balls
= 20 * 10 * 10
= 2000

**Conclusion:**
There are 2000 ways to select 9 balls from 6 red balls, 5 white balls, and 5 blue balls such that each selection consists of 3 balls of each color.

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