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  • In how many ways can 5 balls be selected from 6 identical red balls and 8 identical blue balls?  Option: 1 39<div class=

In how many ways can 5 balls be selected from 6 identical red balls and 8 identical blue balls?

 

Option: 1

39


Option: 2

105


Option: 3

126


Option: 4

210


Answers (1)

To find the number of ways to select 5 balls from 6 identical red balls and 8 identical blue balls, we can use the concept of combinations.

Since the red balls are identical and the blue balls are identical, we only need to consider the number of red balls selected. The remaining balls will be blue.

We can choose 0 to 5 red balls.

 Case1: Selecting 0 red balls

If we don't select any red balls, we need to select all 5 balls from the 8 blue balls. This can be done in only 1 way.

Case 2: Selecting 1 red ball

We choose 1 red ball and 4 blue balls. Since the red balls are identical, there is only 1 combination possible.

Case 3: Selecting 2 red balls

We choose 2 red balls and 3 blue balls. Again, since the red balls are identical, there is only 1 combination possible.

Case 4: Selecting 3 red balls

We choose 3 red balls and 2 blue balls. The number of combinations can be calculated as
6 C_3=20 \mid
Case 5: Selecting 4 red balls

We choose 4 red balls and 1 blue ball. The number of combinations can be calculated as 6 C_4=15 \mid
Case 6: Selecting 5 red balls

We choose 5 red balls and no blue balls. Since there are only 6 red balls available, there is only 1 combination possible.

Now, we can sum up the number of combinations from each case to find the total number of ways to select 5 balls: 
1+1+1+20+15+1=39

 

 

 

Posted by

Kshitij

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