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Mamont248 [21]
3 years ago
15

50 POINTS I NEED THIS IM CONFUSED

Mathematics
1 answer:
Brilliant_brown [7]3 years ago
8 0
Ithe answer is 9 , -7
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Suppose we want to choose 4 colors, without replacement, from 18 distinct colors.
amm1812

Answers:

  • (a) 73440
  • (b)  3060

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

Explanation for part (a)

Consider four slots labeled A,B,C,D.

We have

  • 18 choices for slot A
  • 17 choices for slot B
  • 16 choices for slot C
  • 15 choices for slot D

We started at 18 and counted down until we filled the four slots. The countdown is because we cannot repeat a color. Multiply out those values to get the answer: 18*17*16*15 = 73440

You can use the nPr permutation formula as an alternative method

_nP_r = \frac{n!}{(n-r)!}

in this case n = 18 and r = 4. The exclamation marks indicate factorial.

-----------------------------------

Explanation for part (b)

Let's say we had color labels A,B,C,... all the way up to R which is the 18th letter in the English alphabet. From those 18 letters, we can only pick four. Let's say we pick D,E,F,G.

Focusing solely on the set {D,E,F,G}, we only have one set and the order doesn't matter. So {D,E,F,G} is the same as {D,E,G,F}.

There are 4*3*2*1 = 24 ways to arrange those four items meaning that we'll need to divide the result of part (a) by 24 to get the result of part (b)

73440/24 = 3060

You could use the nCr combination formula to get the same result

_nC_r = \frac{n!}{r!(n-r)!}

where n = 18 and r = 4 are the same from last time.

The connection between nPr and nCr is this

_nC_r = \frac{_nP_r}{r!}

which can be rearranged into

_nP_r = r!*\left( _nC_r \right)

these formulas are handy to help us go back and forth between nCr or nPr.

8 0
3 years ago
Write a word phrase for 49+m
FrozenT [24]
The sum of 49 and m.
8 0
3 years ago
Read 2 more answers
Solve the system (picture) by substitution
Westkost [7]
Try out all of your options by filling the the x and y values from each option. You can use either of the two equations to solve

1) 2(2)+3(3) does not equal 5
2) 2(3)+3(2) does not equal 5
3) 2(3)+3(-2) does not equal 5
4) 2(-2)+3(3) equals 5
4.5) Double check your answer by doing the same thing for the second equation // 3(-2)+2(3) does equal zero.

D
6 0
3 years ago
Distribute. Please help asap
Sholpan [36]

Answer:

-9u^7v - 6u^5v - 21u^2v

Step-by-step explanation:

5 0
3 years ago
The equation of a line is<br> -2x+5t=-20 <br>what is the x-intercept of the line?
vampirchik [111]

The x intercept of the line is at x = 10.

The x intercept is always the value of x when all other values are equal to 0. So in this case, we put 0 in for t and then solve.

-2x + 5t = -20

-2x + 5(0) = -20

-2x = -20

x = 10

8 0
3 years ago
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