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Explanation:
We'll be using the n C r combination function. To make the notation a bit easier to deal with, I will write "C(n,r)" instead of "n C r".
The formula is
C(n,r) = (n!)/(r!*(n-r)!)
where the exclamation marks represent factorials.
A factorial is where you start with a positive integer, and count down to 1 multiplying all along the way.
Examples:
5! = 5*4*3*2*1
8! = 8*7*6*5*4*3*2*1 = 120
Note how the string "5*4*3*2*1" is in both 5! and 8!
We can say 8! = 8*7*6*5!
Because we can replace the "5!" at the end with "5*4*3*2*1" later if we wanted. This strategy is used to help find a shortcut to simplification.
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We have n = 9 appetizers and r = 6 items we can select from this pool.
C(n,r) = (n!)/(r!*(n-r)!)
C(9,6) = (9!)/(6!*(9-6)!)
C(9,6) = (9!)/(6!*3!)
C(9,6) = (9*8*7*6!)/(6!*3*2*1)
C(9,6) = (9*8*7)/(3*2*1) .... the "6!" terms canceled out
C(9,6) = 504/6
C(9,6) = 84
There are 84 ways to choose six appetizers from the pool of nine available
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Repeat those steps for the main courses. Use n = 8 and r = 5 this time.
C(n,r) = (n!)/(r!(n-r)!)
C(8,5) = (8!)/(5!*(8-5)!)
C(8,5) = (8!)/(5!*3!)
C(8,5) = (8*7*6*5!)/(5!*3*2*1)
C(8,5) = (8*7*6)/(3*2*1)
C(8,5) = (336)/(6)
C(8,5) = 56
There are 56 ways to choose five main course meals from the pool of eight available
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Then do the same for the desserts. Use n = 3 and r = 2.
C(n,r) = (n!)/(r!(n-r)!)
C(3,2) = (3!)/(2!*(3-2)!)
C(3,2) = (3!)/(2!*1!)
C(3,2) = (3*2*1)/(2*1*1)
C(3,2) = 6/3
C(3,2) = 3
There are 3 ways to choose two desserts from the pool of three available
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The last step is to multiply all these results:
84*56*3 = 14112
This is the number of ways to select all of the items given the restrictions listed. The order does not matter.
An example of a word problem that can be solved by ordering three decimals to thousandths is determining the order in which three items were purchased based on their prices.
An example of a word problem that can be solved by ordering three decimals to thousandths is:
John bought 3 different items from a store. The prices of the items were $2.345, $2.450, and $2.400 respectively. In what order did John purchase the items from least expensive to most expensive?
To solve this problem, we can order the decimals from least to greatest by looking at the thousandths place. The correct order is $2.350, $2.400, and $2.450.
#SPJ2
Answer:
The quotient of our given numbers is 3.65.
Step-by-step explanation:
We are asked to find the quotient of 43.8 and 12.
To find the quotient of 43.8 and 12, we need to divide 43.8 by 12 as shown below:
Therefore, the quotient of our given numbers would be 3.65.