Small question. When we have multiple combinations or permutations within the same problem, do we add or multiply the individual comb./perm. to get the total number of possibilities ?
Thanks in advance for your help
As mentioned above, it depends on whether it is an 'OR' relation or an 'AND' relation.
I have chosen a red shirt to wear. I have 3 pairs of trousers and 2 pairs of jeans. In how many ways can I choose my dress?
I need to choose either a pair of trousers OR a pair of jeans. This is an OR relation. We need to add here. Total number of ways = 3+2 = 5
I have 4 shirts and 3 pairs of trousers. In how many ways can I choose my dress?
I need to choose 1 shirt AND 1 pair of trousers. This is an AND relation. We need to multiply here. Total number of ways = 4*3 = 12
For every one shirt, you have 3 trousers to choose from so a total of 12 combinations.
Take another example: I have 4 shirts, 3 pairs of trousers and 2 pairs of jeans. In how many ways can I choose my dress?
I have to select 1 shirt AND a pair of trousers OR a pair of jeans.
Total combinations = 4 *(3 + 2) = 20
Similarly, you have 10 boys and 20 girls. In how many ways can you select 2 boys and 2 girls?
You have to select 2 boys AND 2 girls. Multiply.
In 10C2 * 20C2 ways
You have 10 boys and 20 girls. In how many ways can you select 4 people such that they have the same gender?
You can select either 4 boys OR 4 girls. Add.
This can be done in 10C4 + 20C4 ways
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