A combination is an unordered arrangement of r distinct objects in a set of n objects. To find the number of permutations, we use the following equation:
n!/((n-r)!r!)
In this case, there could be 0, 1, 2, 3, 4, or all 5 cards discarded. There is only one possible combination each for 0 or 5 cards being discarded (either none of them or all of them). We will be the above equation to find the number of combination s for 1, 2, 3, and 4 discarded cards.
5!/((5-1)!1!) = 5!/(4!*1!) = (5*4*3*2*1)/(4*3*2*1*1) = 5
5!/((5-2)!2!) = 5!/(3!2!) = (5*4*3*2*1)/(3*2*1*2*1) = 10
5!/((5-3)!3!) = 5!/(2!3!) = (5*4*3*2*1)/(2*1*3*2*1) = 10
5!/((5-4)!4!) = 5!/(1!4!) = (5*4*3*2*1)/(1*4*3*2*1) = 5
Notice that discarding 1 or discarding 4 have the same number of combinations, as do discarding 2 or 3. This is being they are inverses of each other. That is, if we discard 2 cards there will be 3 left, or if we discard 3 there will be 2 left.
Now we add together the combinations
1 + 5 + 10 + 10 + 5 + 1 = 32 choices combinations to discard.
The answer is 32.
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Note: There is also an equation for permutations which is:
n!/(n-r)!
Notice it is very similar to combinations. The only difference is that a permutation is an ORDERED arrangement while a combination is UNORDERED.
We used combinations rather than permutations because the order of the cards does not matter in this case. For example, we could discard the ace of spades followed by the jack of diamonds, or we could discard the jack or diamonds followed by the ace of spades. These two instances are the same combination of cards but a different permutation. We do not care about the order.
I hope this helps! If you have any questions, let me know :)
Step-by-step explanation:
$5 US dollar = L123 Honduran Lempiras
L2300Honduran Lempiras = x ( Let $ be x)
By using chain rule, we get
5×2300 = 123×x
or, 11500 = 123x
or, x = 11500÷123
hence, x = 93.49593496
This is a system of equations.
First, you set everything in terms of y.
Take the first equation and move set everything equal to y
y=0+2x
Since it’s 0, you don’t need to put it, so
y=2x works.
Then, you plug y=2x into the bottom equation, for the y.
-7x +3(2x)=2. You do this because now you have the same variable for both and it can be solved easily.
Then you can simplify.
-7x+3x = 2
Then combine like terms.
-4x = 2
Divide by -4 on each side.
x = -1/2
So, now that you have x, you can plug in your x-value back into the top equation.
-2(-1/2) + y = 0
Combine like terms
1+y=0
Get y by itself
y=-1
There you have it!
You can check by plugging in both values to any of the equations. We will use the top one here.
-2(-1/2) + (-1) =0
+1 + -1 = 0
It works!
So,
X= -1/2
Y= -1
Please rate me Brainliest answer :)
Answer:
(-1,1)
Step-by-step explanation:
