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3 years ago

Winnie has 7 soccer trophies she wants to arrange in an array. How many different arrays are possible?

Mathematics

1 answer:

notka56 [123]3 years ago

7 0

Answer:

5040 possible arrangements

Step-by-step explanation:

Given

$Trophies = 7$

Required

Possible arrangements

The 1st can be placed in any 7 positions

The 2nd, in 6 positions

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Up till the last in 1 position

So, the number of arrangements is:

$Arrangements = 7 * 6 * 5 * 4 * 3 * 2 * 1$

$Arrangements = 5040\ ways$

You might be interested in

Convert the fraction 7 24 into a repeating decimal.

goldenfox [79]

$\dfrac7{24}=\dfrac6{24}+\dfrac1{24}=\dfrac14+\dfrac1{24}$

$\dfrac1{24}=\dfrac1{8\time3}=\dfrac a8+\dfrac b3=\dfrac{3a+8b}{24}$
$\implies3a+8b=1$

We can choose $a=-1$ and $b=\dfrac12$ , so that

$\dfrac1{24}=-\dfrac18+\dfrac16$

Recalling that $\dfrac13=0.333\ldots$ , it follows that $\dfrac16=0.166\ldots$ . So,

$\dfrac1{24}=0.125+0.166\ldots=0.04166\ldots$
$\implies\dfrac7{24}=0.25+0.4166\ldots=0.29166\ldots$

6 0

3 years ago

Simplify the rational expression. Find all numbers that must be excluded from the domain of the simplified rational expression.

BaLLatris [955]

Answer:

y ≠ 9, y ≠ 3

Step-by-step explanation:

y² -12y +27 = (y - 9) (y - 3)

Denominator ≠ 0

y ≠ 9 or y ≠ 3

5 0

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?

grin007 [14]

<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.

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

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