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sladkih [1.3K]
3 years ago
12

Calculate the number of ways to form a set of three distinct items such that no two of the selected items are in the same row or

same column
Mathematics
1 answer:
Eddi Din [679]3 years ago
8 0

Answer:

1200

Explanation:

Order does not matter, if we said xyz order, it would still not make a difference if it was zyx or yzx hence we use the combination formula:

nCr = n! / r! * (n - r)!

where n= total number of items

r= number of items chosen at a time

Combinations are used when the order of events do not matter in calculating the outcome.

We calculate using the formula:

(30×20×12)÷3!=1200

There are therefore 1200 ways for the three distinct items to not be in same row or column

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Sedaia [141]
\bf \begin{array}{cccccclllll}
\textit{something}&&\textit{varies directly to}&&\textit{something else}\\ \quad \\
\textit{something}&=&{{ \textit{some value}}}&\cdot &\textit{something else}\\ \quad \\
y&=&{{ k}}&\cdot&x
&&  y={{ k }}x
\end{array}\\ \quad \\


and also

\bf \begin{array}{llllll}
\textit{something}&&\textit{varies inversely to}&\textit{something else}\\ \quad \\
\textit{something}&=&\cfrac{{{\textit{some value}}}}{}&\cfrac{}{\textit{something else}}\\ \quad \\
y&=&\cfrac{{{\textit{k}}}}{}&\cfrac{}{x}
&&y=\cfrac{{{  k}}}{x}
\end{array}


now, we know that V varies directly to T and inversely to P simultaneously
thus\bf V=T\cdot \cfrac{k}{P}

so     \bf V=T\cdot \cfrac{k}{P}\qquad 
\begin{cases}
V=42\\
T=84\\
P=8
\end{cases}\implies 42=\cfrac{84k}{8}\implies 4=k
\\\\\\
V=\cfrac{4T}{P}\qquad now\quad 
\begin{cases}
V=74\\
P=10
\end{cases}\implies 74=\cfrac{4T}{10}\implies 185=T
7 0
3 years ago
Substitute: 7.5x = 5.5x + 10
Umnica [9.8K]

The value of x is 5

<h3>What are algebraic expressions?</h3>

Algebraic expressions are expressions made up;

  • Factors
  • variables
  • terms
  • constants

They also consist of mathematical operations such as addition, multiplication, division, subtraction, parenthesis, brackets, etc

We have the expression as;

7.5x = 5.5x + 10

collect like terms

7.5x - 5.5x = 10

subtract the like terms

2.0x = 10

Make 'x' the subject

x = 10/2. 0

x = 5

Thus, the value of x is 5

Learn more about algebraic expressions here:

brainly.com/question/4344214

#SPJ1

7 0
1 year ago
A distribution has the five-number summary shown below. What is the range of this distribution? 24, 36, 42, 57, 65
inn [45]
Hello!

To find the range of the distribution, we must order the data from least to greatest (it has already been done) and then subtract the smallest value from the largest value in the set.

In this set, the smallest value is 24, and the largest value is 65. Subtract:

65 - 24 = 41

A N S W E R:

The range of the distribution below is A. 41.
Have a wonderful day!
5 0
3 years ago
Read 2 more answers
Function or not a Function?
iogann1982 [59]

Answer:

not a function

Step-by-step explanation:

the input of K is used more than once

6 0
3 years ago
A table is 2 feet 6 inches long.There are 2.54 centimeters in one inch.What is the length of the table in centimeters? (7.4E,7.1
Nesterboy [21]

Answer:

79.248

Step-by-step explanation:

5 0
2 years ago
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