Solved Examples on Calculation of Combination Probability
Example 1. In a team, 3 boys and 4 girls are there. Among them 4 members need to be selected for one round of a game. Find the probability of selecting an equal number of boys and girls?
Solution:
Probability of selecting an equal number of boys and girls = (4C2 × 3C2)/7C4
(4C2 × 3C2)/7C4 = 18/35
Hence probability of selecting equal number of boys and girls is 18/35
Example 2. What is the number of possible combinations to choose 6 numbers from a set of 49 numbers?
Solution:
49C6 = 49!/6! (49-6)!
49C6 = 49!/(6! × 43!) possible ways.
Example 3. What is the number of ways need to form a group of 3 people from a group of 10?
Solution:
10C3 = 10!/3!(10-3)!
10C3 = 10×9×8/3×2×1
10C3 = 120
∴There are 120 different ways to do this.
Example 4. How many ways can 8 students be chosen from a class of 21?
Solution:
21C8 = 21!/8!×(21-8)!
21C8 = (21×20×19×18×17×16×15×14)/(8×7×6×5×4×3×2×1)
21C8 = 203,490
∴ There are 203,490 ways to chose from a class of 21.
How To Calculate Probability using Combination
Combination probability is a mathematical method that involves the process of combination in determining the number of favorable outcomes of an event. We use combinations in probability problems to determine a sequence of outcomes where the order of the outcomes does not matter. Understanding how to calculate combination probability can be a useful mathematical skill in the field of math and science.
In this article, we will discuss in detail the definitions of combination and probability and how to calculate combination probability with solved examples.
Table of Content
- What is Combination Probability in Math?
- Combination in Math
- What is Probability?
- Formula for Calculating Probability using Combination
- How to Calculate Combination Probability?
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