Question

You are interested in four different extracurricular activities: jazz band, soccer, debate, and theatre. You have time in you schedule for only two activities. How many different combinations of two activities can you pick from the four choices?
a.
6
c.
8
b.
4
d.
12

Answer 1

combination formula

nCr = \[\frac{ n! }{ r!(n-r)! }\]
where n = the # of items to choose from (which is 4 in this case, since there are 4 activities)
and r = the # of items chosen at once (which is 2, since 2 activities are being chosen for the schedule)

Answer 2

alternative method:

4 activities for the first choice
after the first one is chosen, 3 activities left for the second choice ---> 4 * 3 choices
**however** you cannot stop here.

picking jazz band + soccer is the same as picking soccer + jazz band (so the order doesn't matter). therefore, to account for duplicates, you'll have to divide the previous number by 2.