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

2 years ago

What is the missing number<br> 7 x ( ? x 9) = 63

GrogVix [38]

The ? is 1.

7*(9*1)=63

Hope this helps!!

6 0

3 years ago

Find the vertex of the following equation y= (x+9)^2+8​

Find the vertex of the following equation y= (x+9)^2+8