# Combinations problem

• April 26th 2009, 08:16 AM
wheresthecake
Combinations problem

Quote:

A: a freshman has 4 exams to take with 10 examination periods avaialable. how many possible arrangements are there of his exam schedule?

B: from a group of 5 swimmers and 8 runners, an athletic contingent of 7 is to be formed. how many teams are possible if there are to be: b1) 2 swimmers, 5 runners and b2) at least 3 swimmers
• April 26th 2009, 09:48 PM
SengNee
Quote:

Originally Posted by wheresthecake

A:
This should not be combination but permutation.
Because each of 4 exams should not be the same.
$^10P_4$

B:
1)
2 swimmers: $^5C_2$

5 runners: $^8C_5$

$^5C_2 \cdot ^8C_5$

2)
Minimum 3 swimmers.

3 swimmers, 4 runners
4 swimmers, 3 runners
5 swimmers, 2 runners
(Maximum 5 swimmers)

Then find their sum.