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From the set of 6 letters A, B C, D, E and F, there are 20 different 3-letter subsets that could be selected.

What is the number of 3-letter subsets that include the letter F?

I am wondering if someone got a simpler way..

4x6=24

ABF ACF ADF AEF BAF BCF BDF BEF CEF .... ....

First thing you must determine is "are the subsets ordered?". You should be able to tell by the premise that there are only 20 subsets of 3 in 6. If there are NOT ordered, then you are double counting in your analysis. In any case, there is a much easier way. If you know that something must be including in your subset, perhaps the number of ways the OTHER members can be in the group will yield the correct result.... _________________

Best,

AkamaiBrah Former Senior Instructor, Manhattan GMAT and VeritasPrep Vice President, Midtown NYC Investment Bank, Structured Finance IT MFE, Haas School of Business, UC Berkeley, Class of 2005 MBA, Anderson School of Management, UCLA, Class of 1993

Why ABF is same as BAF. Shouldn't they be different.
I understand thet 6C3 gives 20. Similarly other two letters from the set of 5 can be choosen in 5C2 ways = 10.
If you consider ABF to be same as BAF then this answer is correct.Otherwise lot many combinations are possible.
I hope some can explain why BAF is same as ABF. The question does not mention anything about mere presence of the letter without any order.

Originally posted on MIT Sloan School of Management : We are busy putting the final touches on our application. We plan to have it go live by July 15...