# What is the importance of the Fundamental Principles of Counting?

• Last Updated : 29 Dec, 2021

Probability defines the measure of the occurrence of a likable event out of all the possible results/outcomes of that event. The probability of an event always ranges between 0 to 1. When Probability is zero it signifies that there is no chance for the favorable/likable outcome to occur. And on the other hand, when Probability is one, it signifies that there is a certainty that every time the likable outcome will appear as the outcome of the event. Knowledge of Numbers thus becomes very important when considering Probability scenarios.

### The fundamental principle of counting

The Fundamental Probability of Counting suggests that if there is a probability scenario where there are x1, x2, x3 … xn entity objects each with y1, y2, y3 … yn choices available for each of the entity then the number of ways,

Ways = y1 × y2 × y3 × … × yn

Here, the choices for each available entity are multiplied to get the total ways of selection.

### What is the importance of the Fundamental Principles of Counting?

The Fundamental Principle of Counting is essential as it has the below characteristics:

• Fundamental Principle of Counting  helps to determine how selection is done on the basis of available choices.
• Fundamental Principle of Counting simplifies the approach of selection considering all the possible choices and their combinations for calculating the Probability.
• The Fundamental Principle of Counting is one such vital part of Probability which deals with the knowledge of numbers and there much-needed use when considered from the knowledge of Mathematics.

Example of Fundamental Counting Principle Problem, Consider Seema has 2 blue pens, 2 black and 2 red pens. In how many ways can she select one pen of each kind,

Then pairing can take place as follows:

(B1 b1 r1), (B1 b1 r2), (B1 b2 r1), (B1 b2 r2), (B2 b1 r1), (B2 b1 r2), (B2 b2 r1), (B2 b2 r2)

The total number of ways of choosing this pairing using Counting Principle Problems,

• Choices available for  blue pens = 2
• Choices available for black pens = 2
• Choices available for red pens = 2

Total number of ways: 2 × 2 × 2 = 8

### Similar Problems

Question 1: Does Fundamental Counting Principle always hold for Counting Problems.

Yes, Fundamental Counting Principle always holds for Counting Problems.

Question 2: Consider a teacher who has 1 black and 2 red pens. In how many ways can she select one pen of each kind.

Solution:

Then pairing can take place as follows,

(B1 R1), (B1 R2)

• Choices available for black pens = 1
• Choices available for red pens = 2

Total number of ways: 1 × 2 = 2

Question 3: Consider a boy has choice of selecting between 2 cups of tea and 2 cups of coffee. In how many ways can he select one cup of each kind.

Solution:

Then pairing can take place as follows,

(T1 C1), (T1 C2), (T2 C1), (T2 C2

• Choices available for tea = 2
• Choices available for coffee = 2

Total number of ways: 2 × 2  = 4

Question 4: Consider a child has 3 lollipop and 2 toffees. In how many ways can she select one candy of each kind.

Then pairing can take place as follows,

(L1 T1), (L1 T2), (L2 T1), (L2 T2), (L3 T1), (L3 T2)

• Choices available for black pens = 3
• Choices available for red pens = 2

Total number of ways: 3 × 2 = 6

Question 5: Consider a girl has 3 black tops and 2 blue lowers. In how many ways can she select a dress combo of top and lower.

Solution:

Then pairing can take place as follows:

(B1 b1), (B1 b2), (B2 b1), (B2 b2), (B3 b1), (B3 b2)

• Choices available for black tops = 3
• Choices available for blue lowers = 2

Total number of ways: 3 × 2 = 6

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