All categories

3 years ago

A swim team must be chosen from 12 candidates. What is the greatest number of different 3-person teams that can be chosen?

Mathematics

2 answers:

grin007 [14]3 years ago

8 0

<h3>Answer: 220 combinations</h3>

==========================================

Explanation:

We have 12*11*10 = 1320 permutations possible. This is where order matters. However, order does not matter with swim teams as there are no positions or ranks. All that matters is the group overall (rather than any individual in the group).

Consider the set {A,B,C}. We have 3*2*1 = 6 ways to arrange this set of letters. When considering a permutation, there are 6 permutations but only 1 combination since order doesnt matter and ABC is the same as BAC. Therefore, we divide 1320 over 6 to get the final answer of 1320/6 = 220.

---------

You can use the combination formula with n = 12 and r = 3. Doing so will give the following:

$_n C _r = \frac{n!}{r!*(n-r)!}\\\\_{12} C _3 = \frac{12!}{3!*(12-3)!}\\\\_{12} C _3 = \frac{12!}{3!*9!}\\\\_{12} C _3 = \frac{12*11*10*9!}{3!*9!}\\\\_{12} C _3 = \frac{12*11*10}{3!}\\\\_{12} C _3 = \frac{12*11*10}{3*2*1}\\\\_{12} C _3 = \frac{1320}{6}\\\\_{12} C _3 = 220\\\\$

As you can see, we get the same result and note how 1320/6 is also present as well.

navik [9.2K]3 years ago

7 0

It should be the 220 combinations

You might be interested in

the function intersects its midline at (-pi,-8) and has a maximum point at (pi/4,-1.5) write an equation

Tcecarenko [31]

The equation that represents the sinusoidal function is $x(t) = -8 + 6.5 \cdot \sin \left[\left(\frac{2}{3} \pm \frac{4\cdot i}{3}\right)\cdot t + \left(\frac{2\pi}{3} \pm \frac{7\pi \cdot i}{3} \right)\right]$ , $i\in \mathbb{Z}$ .

<h3>Procedure - Determination of an appropriate function based on given information</h3>

In this question we must find an appropriate model for a periodic function based on the information from statement. Sinusoidal functions are the most typical functions which intersects a midline ( $x_{mid}$ ) and has both a maximum ( $x_{max}$ ) and a minimum ( $x_{min}$ ).

Sinusoidal functions have in most cases the following form:

$x(t) = x_{mid} + \left(\frac{x_{max}-x_{min}}{2} \right)\cdot \sin (\omega \cdot t + \phi)$ (1)

Where:

$\omega$ - Angular frequency
$\phi$ - Angular phase, in radians.

If we know that $x_{min} = -14.5$ , $x_{mid} = -8$ , $x_{max} = -1.5$ , $(t, x) = (-\pi, -8)$ and $(t, x) = \left(\frac{\pi}{4}, -1.5 \right)$ , then the sinusoidal function is:

$-8 +6.5\cdot \sin (-\pi\cdot \omega + \phi) = -8$ (2)

$-8+6.5\cdot \sin\left(\frac{\pi}{4}\cdot \omega + \phi \right) = -1.5$ (3)

The resulting system is:

$\sin (-\pi\cdot \omega + \phi) = 0$ (2b)

$\sin \left(\frac{\pi}{4}\cdot \omega + \phi \right) = 1$ (3b)

By applying inverse trigonometric functions we have that:

$-\pi\cdot \omega + \phi = 0 \pm \pi\cdot i$ , $i \in \mathbb{Z}$ (2c)

$\frac{\pi}{4}\cdot \omega + \phi = \frac{\pi}{2} + 2\pi\cdot i$ , $i \in \mathbb{Z}$ (3c)

And we proceed to solve this system:

$\pm \pi\cdot i + \pi\cdot \omega = \frac{\pi}{2} \pm 2\pi\cdot i -\frac{\pi}{4}\cdot \omega$

$\frac{3\pi}{4}\cdot \omega = \frac{\pi}{2}\pm \pi\cdot i$

$\omega = \frac{2}{3} \pm \frac{4\cdot i}{3}$ , $i\in \mathbb{Z}$ $\blacksquare$

By (2c):

$-\pi\cdot \left(\frac{2}{3} \pm \frac{4\cdot i}{3}\right) + \phi =\pm \pi\cdot i$

$-\frac{2\pi}{3} \mp \frac{4\pi\cdot i}{3} + \phi = \pm \pi\cdot i$

$\phi = \frac{2\pi}{3} \pm \frac{7\pi\cdot i}{3}, i\in \mathbb{Z}$ $\blacksquare$

To learn more on functions, we kindly invite to check this verified question: brainly.com/question/5245372

5 0

2 years ago

If ur skinny so what! if ur chubby so what!!

jenyasd209 [6]

Lowkey made ma day - love you

3 0

2 years ago

Andrew and Kate have $30 to spend on dinner, tax, and gratuity at Mo’s Restaurant. Tax is 6%, and they will give a 15% tip on th

Anton [14]

Answer:

yes, the meal costs 25.60

Step-by-step explanation:

I used a slightly different method but B (Yes. They have enough to pay their bill: 21 dollars times 1.06 = 22 dollars and 26 cents and 22 dollars and 26 cents times 1.15 = 25 dollars and 60 cents.) is correct.

21*0.06=1.26

1.26+21=22.26

22.26*0.15=3.34

22.26+3.34=25.60

4 0

2 years ago

Read 2 more answers

A computer magazine is analyzing three microprocessors. Microprocessor A executes one cycle in 0.00000000003 seconds, microproce

solong [7]

Answer:

I don't understand

Step-by-step explanation:

6 0

3 years ago

Help plsssssssssssss

Rina8888 [55]

Answer:

Answer:OPTIONS

Answer:OPTIONS3 D

Answer:OPTIONS3 D4 D

Answer:OPTIONS3 D4 D5 B

Answer:OPTIONS3 D4 D5 BStep-by-step explanation:

Answer:OPTIONS3 D4 D5 BStep-by-step explanation:MEAN IS =SUM OF ALL NO.S /TOTAL.NO'S(AVERAGE)

Answer:OPTIONS3 D4 D5 BStep-by-step explanation:MEAN IS =SUM OF ALL NO.S /TOTAL.NO'S(AVERAGE)FIRST WE FIND SUM OF ALL NO. 

Answer:OPTIONS3 D4 D5 BStep-by-step explanation:MEAN IS =SUM OF ALL NO.S /TOTAL.NO'S(AVERAGE)FIRST WE FIND SUM OF ALL NO. MEDIAN=AVERAGE OF MIDDLE TERMS

3 0

3 years ago