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 :)
To find the rate in miles per hour, divide the miles by the hours.
(1 1/2 miles)/(3/5 hour) =
= 3/2 miles * (5/3 hour)
= 5/2 mph
= 2 1/2 mph
Her walking rate is 2 1/2 mph.
(4 1/2 miles) / ( 2 1/2 mph) =
= 9/2 miles / (5/2 mph)
= 9/2 * 2/5 hours
= 9/5 hours
= 1 4/5 hours
From 9:00 a.m. to 11 a.m., she has 2 hours, but she only needs 1 4/5 hours to walk, so she will make it to work on time.
Answer:
20/3 ounces of water is added.
Step-by-step explanation:
how many ounces of pure water should be added to 20 ounces of 40% solution of muriatic acid to obtain a 30% solution of muriatic acid?
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The acid is 40% of 20 ounces = 8 ounces.
0.4*20 = 8
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That same 8 ounces is to be 30%. The water will be the other 70%.
8/30 = x/100
30x = 800
x = 80/3, the total amount of the solution.
We started with 20, so 80/3 - 20 = 20/3
20/3 ounces of water is added.
Answer:
<h2>
The situation involves permutation</h2><h2>
The number of arrangement is 120</h2>
Step-by-step explanation:
Given that
Algebra book=1
Geometry book=1
Chemistry book= 1
English book= 1
Health book= 1
Total number of books N = (1+1+1+1+1)= 5
Permutation is used to determines the number of possible arrangements in a set when the order of the arrangements is crucial.
Number of arrangements = N!
Number of arrangements= 5*4*3*2*1= 120
