SOLUTION: Three letters are to be chosen from the word BIOLOGY. Find the number of ways if a) it contains both the letters O

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Question 1082376: Three letters are to be chosen from the word BIOLOGY.
Find the number of ways if
a) it contains both the letters O
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
Does order matter?

Do you consider [OBO], [OOB], and [BOO], as 1 choice or as 3 choices?

We must know whether they are considered different or all the same.

If it is one choice then there are only 5 ways:

{B,O,O}, {I,O,O}, {L,O,O}, {G,O,O}, and {Y,O,O} 

If it is three choices then there are 15 ways:

BOO, OBO, OOB,
IOO, OIO, OOI,
LOO, OLO, OOL,
GOO, OGO, OOG,
YOO, OYO, OOY.

Edwin