8. The bottom part of this block is a rectangular prism. The top part is a square pyramid. You want to
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The number of possible seats is an illustration of permutation
There are 1728 possible sitting arrangements
<h3>How to determine the number of seats</h3>From the question, we have the following highlights:
- Chris can only take 1 seat (i.e. the central seat)
- Jo can take 2 seats (i.e. the seats adjacent the central seat)
- Alex, Barb and Dave can take 3! number of seats
- Eddie, Fred, and Gareth can take 3! number of seats on the right of Chris.
- The remaining 4 adults do not have preference, then they can seat in 4! ways
So, the number of sitting arrangement is:
Evaluate the product
Hence, there are 1728 possible sitting arrangements
Read more about permutation at:
Answer:
Step-by-step explanation:
Both expressions are examples of the <em>distributive property</em>, which basically says "if I have <em>this </em>many groups of some size and <em>that</em> many groups of the same size, I've got <em>this </em>+ <em>that</em> groups of that size altogether."
To give an example, if I've got <em>3 groups of 5 </em>and <em>2 groups of 5</em>, I've got 3 + 2 = <em>5 groups of 5 </em>in total. I've attached a visual from Math with Bad Drawings to illustrate this idea.
Mathematically, we'd capture that last example with the equation
. We can also read that in reverse: 3 + 2 groups of 5 is the same as adding together 3 groups of 5 and 2 groups of 5; both directions get us 8 groups of 5. We can use this fact to rewrite the first expression like this:
.
This idea extends to subtraction too: If we have 3 groups of 4 and we take away 1 group of 4, we'd expect to be left with 3 - 1 = 2 groups of 4, or in symbols: . When we start with two numbers like 15 and 10, our first question should be if we can split them up into groups of the same size. Obviously, you could make 15 groups of 1 and 10 groups of 1, but 15 is also the same as <em>3 groups of 5</em> and 10 is the same as <em>2 groups of 5</em>. Using the distributive property, we could write this as
, so we can say that
.
