Question

help! in how many ways can 15 basketball players be listed in a program?

a. 1,307,674,368,000
b. 15
c. 32,432,400
d. 1

Answer 1

\[15!\]

Answer 2

15 is right

Answer 3

15 choices for the first one
14 for the second
13 for the third
12 for the fourth
etc
etc

Answer 4

not \(15\) but rather \(15!\)

Answer 5

by the counting principle it is
\[15\times 14\times 13\times 12\times11\times 10\times 9\times 8\times 7\times 6\times 5\times 4\times 3\times 2\times 1=15!\]

Answer 6

ou have 15 slots, each of which will hold one of the names of the players. You need to fill the first slot with some name. It doesn't matter which name, so you have 15 names to choose from.

Answer 7

There are n! ways to permute an n element collection. So for this problem, there are 15 different people and you are looking for all the different orderings, or permutations, of those 15 people. The answer is 15!, but to see why consider the following:

You have 15 slots, each of which will hold one of the names of the players. You need to fill the first slot with some name. It doesn't matter which name, so you have 15 names to choose from.

Next, you need to fill the second slot from any of the remaining players. Since you have already selected one of the names from the previous step, you only have 14 names remaining, so there are 14 ways to fill this slot.

Similarly, you need to fill the third slot. You have used two of the names from the previous two steps, so now you have 13 names to choose from, which means you have 13 ways to fill this slot.

This continues for each of the remaining twelve slots. Each slot you have one less name to choose from since each step uses one name.

This can be viewed as the following, where each number represents the way of filling one of the slots:

= 15 * 14 * 13 * 12 * 11 * 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1

= +15%21+

= 1,307,674,368,000

Answer 8

oh ok I get it now. thanks for the help!

Answer 9

http://www.wolframalpha.com/input/?i=15!

Answer 10

your welcome http://www.algebra.com/algebra/homework/Probability-and-statistics.faq.question.614747.html