a bag contains 6 white and 4 Black balls three balls are drawn from the bag find the probability that all of the same colour
<kindly teach with combination method
Answers
Answer:
Step-by-step explanation:
Let S be the sample space
Then n(S)= number of ways of drawing 2 balls out of (6+4)=10
⇒
10
C
2
=
2×1
10×9
=45
Let E= event of getting both balls of same color
Then,n(E)= no of ways (2 balls out of six) or (2 balls out of 4)
=
6
C
2
+
4
C
2
=
2×1
6×5
+
2×1
4×3
=15+6=21
∴P(E)=
n(S)
n(E)
=
45
21
=
15
7
The probability of getting same colour ball is 24
Explanation:
Given Condition:
1. A bag contains 6 white and 4 Black balls
2. Three balls are drawn from the bag
To find:
The probability that all of the same colour
Formula:
Combination Method : n!/r!(n-r)!
According to 1st condition,
The probability that all of the same colour
==> White three or Black is the probability
Using Combination method,
==> White three or Black is the probability
==> Total white ball is 6 and Total Black ball is 4
==> ⁶C₃ or ⁴C₃
==> Or means adding both the Combination
==> ⁿCr = ⁶C₃ or ⁴C₃
==>⁶C₃ , n = 6 and r =3
==>⁴C₃, n = 4 and r=3
==> n!/r!(n-r)! = ⁶C₃ or ⁴C₃
==> n!/r!(n-r)! = ⁶C₃ + ⁴C₃
==> 6!/3!(6-3)! + 4!/3!(4-3)!
==> 6!/3!(3)! + 4!/3!(1)!
==>6! = 6×5×4×3×2×1
==>3! = 3×2×1
==> 4! = 4×3×2×1
==> (6×5×4×3×2×1)/ 3!(3×2×1) +4×3×2×1/3×2×1
==> 6×5×4/3! + 4
==> 6×5×4/3×2×1 +4
==> 2×5×2+4
==> 20+4
==> 24
The probability of getting same colour ball is 24