Question

A swimming coach needs to choose a team for a relay race. The coach must select 4 of 6 available swimmers

and put them in a strategic sequence.
How many unique ways are there to arrange 4 of the 6 swimmers?

Answer 1

There are 15 unique ways to arrange 4 out of the 6 swimmers for the relay race.

Step-by-step explanation:

To find the number of unique ways to arrange 4 out of 6 swimmers, we can use the combination formula.

The formula for combinations is given by nCr = n! / (r!(n-r)!), where n is the total number of swimmers and r is the number of swimmers we want to choose.

In this case, we have 6 swimmers and we want to choose 4 of them, so the calculation would be -

6C4 = 6! / (4!(6-4)!) = 6! / (4!2!)

= (6 x 5 x 4 x 3) / (4 x 3 x 2 x 1)

= 15.

Therefore, there are 15 unique ways to arrange 4 out of the 6 swimmers for the relay race.

Answer 2

360

Step-by-step explanation:

6!/(6-4)!