How do I solve the following questions?
- a) Three letters are to be selected from the letters in the word CONSTANT. How many different combinations are there?
b) Three letters are to be selected from the letters in the word JUGGLING. How many different combinations are there?
Just some questions I have come across preparing for a test.
I have attempted to list the individual letter cases and how many different ways there are of choosing the three (i.e. Choose 3 different letters for CONSTANT or two identical from CONSTANT), however, I would like clarification on this technique to make sure my method is correct.
Your approach is correct. You are basically making a case for each way to get three letters, and then adding all of these individual cases together. Number of letters in CONSTANT is 6
Hence, number of 3 letter words is $${6 \choose 3}.3! + {2 \choose 1}.{5 \choose 1}.3$$