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 :)
y2 - y1 / x2 - x1 = slope
2 - -2 / 2 - -1
4/3
<u>the slope of the line is 4/3</u>
.3455 is the correct answer.
Answer:
Her proportion does not have corresponding parts in the same position.
Step-by-step explanation:
Sharon is drawing up a plan for building a reduced Eiffel Tower on her backyard patio. She has room to make a base of 5 feet. Her work is shown below.
What was Sharon’s error in finding the missing height measurement for her reduced tower?
Her proportion does not have corresponding parts in the same position.
For cross products, she needed to multiply 1050(328) and 5(x).
She needed to divide both sides by 1640, instead of 1050.
She needed to round down to 1.5 feet.
Height : base = 1,050 : 328
She has room to make a base of 5 feet.
Height : base = x : 5
1,050 : 328 = x : 5
1,050 / 328 = x / 5
Cross product
1,050 * 5 = 328 * x
5,250 = 328x
Divide both sides by 328
x = 5250 / 328
= 16.006
Approximately 16
Sharon's error:
Her proportion does not have corresponding parts in the same position.
Answer:
209259
Step-by-step explanation:
45200 / 21.6 = 209259.259259
209259.259259 rounded to nearest whole number = 209259
