Formula for Calculating Probability using Combination

To calculate combination probability, it is important to use the correct formula to find the probability of a specific outcome. There are four formula’s to calculate the probability. They are,

Among the above mentioned formulas, the two most important are,

Combination with Repetition

When repetition is allowed, you can use the following equation to find out the number of combinations,

(r+n-1)!/r!(n-1)!

where,

• n = total number of outcomes of a set
• r = total possible number of outcomes at a time.

Example: Total number of balls in the pool= n = 5. The number of balls to be selected = r = 4, where the selection of balls can be repeated. The order of selection does not matter. Find the number ways the ball can be selected?

Solution:

We will use the formula, ⁿC_r = (r+n-1)!/r!(n-1)!

Now, putting the values we get, ⁵C₄ = (4+5-1)! / 4!·(5-1)!

= 8! / 4!·4! = 8×7×6×5 / 4×3×2×1 = 70

∴ There are 70 possible ways to select the ball.

Combination without Repetition

When repetition is not allowed, you can use the following equation to find out the number of combinations,

n!/(n-r)!r!

where,

• n = total number of outcomes of a set
• r = total possible number of outcomes at a time

Example: The principle would like to assemble a committee of 6 students from the 11 member student council. How many different committees can be chosen?

Solution:

We will use the formula, where, ⁿC_r = n!/(n-r)!r!

Now, after putting thee values we get, ¹¹C₆ = 11!/(11-6)!·6!

= 11! / 5!·6! = 11×10×9×8×7 / 5×4×3×2×1 =66×7 = 462

∴ 462 committees can be chosen.

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.