A swim meet has 13 contestants signed up. To calculate the arrangement of first 6 swimmers in first heat we will use combinations because order doesn't matter.

So to select 6 swimmers out of 13 contestants number of different ways

= $^{13}C_{6}$

= $\frac{13!}{(6!)(13-6)!}$

= $\frac{13\times 12\times 11\times 10\times 9\times 8\times 7!}{6!\times 7!}$

= $\frac{13\times 12\times 11\times 10\times 9\times 8}{6\times 5\times 4\times 3\times 2\times 1}$

= $\frac{1235520}{720}$

= 1716

Therefore, 6 swimmers in the first heat can be arranged in 1716 different ways.

5 0

3 years ago

Lionel created a picture to hang on his wall. The drawing is below. Each circle has a radius of 8cm. The circles touch each othe

Vikki [24]

Answer:

888888

Step-by-step explanation:

88888888888888888888

7 0

2 years ago

Read 2 more answers

A company manufactures and sells personalized stationery. The weekly fixed cost is $3850 and it cost $3.00 to produce each packa

Sveta_85 [38]

Answer:

more than 1100

Step-by-step explanation:

The contribution margin for each package sold is ...

$6.50 -3.00 = $3.50

The number of packages that must be sold to cover fixed costs is ...

3.50n > 3850

n > 1100 . . . . . . . divide by 3.50

The company will generate a profit if more than 1100 packages are produced and sold each week.

_____

<em>Additional comment</em>

If exactly 1100 packages are sold, then costs are covered, but profit is 0. In order for profit to be positive, more than 1100 packages must be sold.

5 0

2 years ago