A box contains 5 pink , 3 green and 2 yellow balls, Three balls are picked up randomly. What is the probability that none of the ball drawn is green

5 টি pink, 3 টি green ও 2 টি yellow সহ মোট বলের সংখ্যা 10 টি।

নির্বিআারে 3 টি বল তোলা বলটি green না হওয়ার সম্ভাবনা = ^{(5 + 2)} C₃ / ¹⁰C₃ = ⁷C₃/¹⁰ C₃

= ( 7! / 3! 4!) / ( 10! / 3! 7!)

= 7!/ 3! 4! × 3! 7!/10!

= 7 × 6 × 5 / 10 × 9 × 8

= 7/24

To find the probability that none of the balls drawn are green when picking 3 balls from a box containing 5 pink, 3 green, and 2 yellow balls, follow these steps:

Total Number of Balls:
- Pink: 5
- Green: 3
- Yellow: 2
- Total balls = 5 + 3 + 2 = 10

Total Number of Ways to Pick 3 Balls Out of 10:
The total number of ways to pick 3 balls out of 10 is given by the combination formula \( \binom{10}{3} \).

\[
\binom{10}{3} = \frac{10!}{3!(10-3)!} = \frac{10 \times 9 \times 8}{3 \times 2 \times 1} = 120
\]

Number of Ways to Pick 3 Balls with No Green Balls:
- Total balls that are not green = 5 (pink) + 2 (yellow) = 7
- We need to pick 3 balls from these 7 balls.

The number of ways to pick 3 balls out of 7 is given by \( \binom{7}{3} \).

\[
\binom{7}{3} = \frac{7!}{3!(7-3)!} = \frac{7 \times 6 \times 5}{3 \times 2 \times 1} = 35
\]

 Probability Calculation:
The probability that none of the balls drawn is green is the ratio of the number of favorable outcomes to the total number of outcomes.

\[
\text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{\binom{7}{3}}{\binom{10}{3}} = \frac{35}{120} = \frac{7}{24}
\]

Answer:
The probability that none of the balls drawn is green is \( \frac{7}{24} \).