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 :)
Answer:
area: 41.04 cm² ; perimeter 35.8 cm
Step-by-step explanation:
Perimeter of shaded area = 1/4 perimeter of circle + line AC = ¼ * 3.14 * 2 * 12 + √(12² + 12²) = 18.84 + 12√2 cm = 35.8 cm
Area of Shaded Region = 1/4 area of circle - area of triangle = ¼ * 3.14 * 12² - ½ . 12 * 12
= (¼ * 3.14 - ½) * 12² = 41.04 cm²
Answer:
Step-by-step explanation:
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The right angle triangles are:
Triangle A has two acute angles and one ninety degree angle
Triangle d has two acute angles and one ninety degree angle.
<h3>What are right triangles?</h3>
A triangle is a three-sided polygon with three edges and three vertices. the sum of angles in a triangle is 180 degrees. A right angled triangle is a triangle in which one of its angles measure 90 degrees.
To learn more about triangles, please check: brainly.com/question/22949981
#SPJ1
1,099= 1,100
HOPE THIS HELPS!!!
