Samacheer Kalvi Class 6 Maths Solutions Term 1 Chapter 6 Information Processing Exercise 6.1

Question 1. Suppose, you have two pairs of shorts, one is black and the other one is blue; three shirts which are white, blue and red. You again wish to make different combinations, but you always want to make sure that the shorts and shirt that you wear are of different colours. List and check how many combinations are possible now.
Answer: There are 5 possible combinations where the shorts and shirt are of different colours. We have two pairs of shorts (black and blue) and three shirts (white, blue, and red). The rule is that the shorts and shirt must always be different colours.
The possible combinations are:
1. Black shorts with White shirt
2. Black shorts with Blue shirt
3. Black shorts with Red shirt
4. Blue shorts with White shirt
5. Blue shorts with Red shirt
For example, combining blue shorts with a blue shirt is not allowed because the colours are the same. This shows how important it is to follow all conditions mentioned.
In simple words: You have two shorts and three shirts. You need to make outfits where the shorts and shirt are not the same colour. There are 5 such unique outfits you can make.

🎯 Exam Tip: Always pay close attention to all conditions mentioned in the question, especially constraints like "different colours" or "not exceeding a certain limit," as these directly affect the number of possible outcomes.

Question 2. You have two red and two blue blocks. How many different towers can you build that are four blocks high using these blocks? List all the possibilities.
Answer: You can build 6 different towers that are four blocks high using two red (R) and two blue (B) blocks. This type of problem involves arranging items where some are identical. Finding all possible arrangements helps in understanding permutations.
Here are all the possible combinations for the towers:
1. R-B-R-B
2. R-R-B-B
3. B-R-R-B
4. B-R-B-R
5. B-B-R-R
6. R-B-B-R
Each listed sequence shows a unique arrangement of the four blocks.
In simple words: If you have two red blocks and two blue blocks, you can make 6 different tall stacks (towers) by changing their order. Each stack must be 4 blocks high.

🎯 Exam Tip: When listing arrangements, be systematic to avoid missing any possibilities. You can imagine building the tower step-by-step or using a tree diagram to cover all sequences.