If these two shapes are similar, what is the measure of the missing length g?

Mathematics

1 answer:

Sophie [7]3 years ago

4 0

So if the shapes are similar, they have to have a number multiple from to get the other triangle. If you divide 63 by 42, you get 1.5. Then you have to divide 54 by 1.5 to get G and that would be 36.

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Suppose we want to choose 4 colors, without replacement, from 18 distinct colors.

amm1812

Answers:

(a) 73440
(b) 3060

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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.

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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

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