In the previous post we have discussed about Differentials Calculus and In today's session we are going to discuss about combination formula. Combination is a technique we use for the purpose of counting the number of ways we can have probable arrangements for the given events. In probability also we would find the use of combination a lot. The combination formula is written as follows:
If we have N events and we wish to select b possible events from N, then we would write it as:
NC b = N! / b! (N – b)!
To solve the formula for combination we must have knowledge of how to expand a factorial of any number. Let us consider an example of combination as follows:
Example: In how many ways we can select 2 black and 4 red balls from a container which contains 10 black and 10 red balls.
Solution: It is been given that the container contains 20 balls in total out of which 10 are black and the rest 10 are red. To select 2 black balls from the container we must use the combination formula for 10 black balls. So, the number of ways we can choose two black balls out of 10 is equal to 10 C 2. Similarly, the number of ways to choose 4 red balls from the 10 red balls is equal to 10 C 4. So, finally we get the total number of ways of selecting 2 black and 4 red balls from the container of 10 black and 10 red balls as:
10C 2 + 10 C 4 = 10! / 2! (8)! + 10! / 4! (6)! = 10 x 9 /2 + 10 x 9 x 8 x 7 /24 = 45 + 210 = 255 ways.
Next we discuss the concept of how to calculate density. Density can be calculated by using a simple formula: Density = Mass /Volume. These concepts are important from the perspective of icse syllabus for class 8.
If we have N events and we wish to select b possible events from N, then we would write it as:
NC b = N! / b! (N – b)!
To solve the formula for combination we must have knowledge of how to expand a factorial of any number. Let us consider an example of combination as follows:
Example: In how many ways we can select 2 black and 4 red balls from a container which contains 10 black and 10 red balls.
Solution: It is been given that the container contains 20 balls in total out of which 10 are black and the rest 10 are red. To select 2 black balls from the container we must use the combination formula for 10 black balls. So, the number of ways we can choose two black balls out of 10 is equal to 10 C 2. Similarly, the number of ways to choose 4 red balls from the 10 red balls is equal to 10 C 4. So, finally we get the total number of ways of selecting 2 black and 4 red balls from the container of 10 black and 10 red balls as:
10C 2 + 10 C 4 = 10! / 2! (8)! + 10! / 4! (6)! = 10 x 9 /2 + 10 x 9 x 8 x 7 /24 = 45 + 210 = 255 ways.
Next we discuss the concept of how to calculate density. Density can be calculated by using a simple formula: Density = Mass /Volume. These concepts are important from the perspective of icse syllabus for class 8.
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