Question 1005321: Four distinct letters are to be chosen from the set
{A, B, C, D, E, F, G, H}
Determine the number of ways to obtain a subset that includes each of the following
(1) the letter C
(2) both E and F
(3) either E or F, but not both
Answer by Edwin McCravy(20054)   (Show Source):
You can put this solution on YOUR website! Four distinct letters are to be chosen from the set
{A, B, C, D, E, F, G, H}
Determine the number of ways to obtain a subset that includes each of the following
(1) the letter C
Choose the C 1 way and the other 3 from these 7 {A, B, D, E, F, G, H}
Answer 1*7C3 = 35 ways
(2) both E and F
Choose them 1 way and choose the other 2 from these 6: {A, B, C, D, G, H}
Answer: 1*6C2 = 15 ways
(3) either E or F, but not both
Case 1: Choose E 1 way and the other 3 from these 6 {A, B, C, D, G, H}
That's 1*6C3 = 20 ways
Case 2: Choose F 1 way and the other 3 from these 6 {A, B, C, D, G, H}
That's also 20 ways.
Answer: 20*2 = 40 ways.
Edwin
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