Hi,
It is ok to feel a little confused since you are new to
the topic.
Consider two situations:
1. Arrange 3 items out of 5 (say, a, b, c, d, e).
2. Select 3 items out of 5 (say, a, b, c, d, e).
Situation 1 is an instance of permutation (note the
keyword 'arrange'). Situation 2 is an instance of combination (note
the keyword 'select').
In situation 1, number of ways = 5 x 4 x 3 = 60.
In situation 2, number of ways = 5C3 = (5!) / [(3!)(2!)]
= 10.
In situation 2, we are not interested in the order of the
3 items selected and we can list systematically the 10
possibilities as follow:
a, b, c
a, b, d
a, b, e
a, c, d
a, c, e
a, d, e
b, c, d
b, c, e
b, d, e
c, d, e
In situation 1, order matters, say, when we arrange the 3
items a, b, c. This could be done in 6 ways:
a, b, c
a, c, b
b, a, c
b, c, a
c, a, b
c, b, a
Thanks.
Cheers,
Wen Shih
So we just look at the keywords in the question?
If the question says select 3 balls out of 6 distinct balls ,
and arrange them in a row, then we will apply both? :)
