From the set of letters A B C D E and F, there are 20 different 3-lett

Question

From the set of 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 F?

A. 8
B. 10
C. 12
D. 15
E. 16

chetan2u · Answer

Since we are looking at sub-sets, the question talks of combination or selection.
Now F is already selected and we have to choose 2 from remaining 5 => 5C2=10

B

Kinshook · Answer

Given: From the set of letters A B C D E and F, there are 20 different 3-letter subsets that could be selected. 
Asked: What is the number of 3-letter subsets that include F?

Since F is already select, we have to select 2 out of remaining 5 letters.
Number of 3-letter subsets that include F = 5C2 = 10

IMO B

abhinavsodha800 · Answer

I did this way is it correct ?

We already know that there are 20 ways to select subset of 3 so to include all subset with F i have subtracted the one's which does not include F from 20 so my equation 20 - 5C3 (After excluding F i will be left with 5 letter n i have to select 3 subsets) .

mtvmtv · Answer

Why would we even have to add any of those formulas, esp. in the response above?

3/6 = 0.5 -> each letter is in the selection 50% of the time -> 20/2 = 10

From the set of letters A B C D E and F, there are 20 different 3-lett

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From the set of letters A B C D E and F, there are 20 different 3-lett

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