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 :)
If you would like to complete the factorization, you can do this using the following steps:
<span>4p^2 + 36p + 81 = (2p + 9) * (2p + 9) = (2p + 9)^2
</span>
The correct result would be 9.
Answer:
1,2,3,6,9,18
Step-by-step explanation:
The multiples of 18 are 1,2,3,6,9,18 or 1*18, 2*9, and 3*6. 5 is not so that eliminates A,B,C and E But 0 or 10, 20, and 30 aren't either.
Answer:
285.6 square units
Step-by-step explanation:
The shaded area can be described a a whole circle less a 90° segment, or as a 3/4 circle with a right triangle added. The formula for the segment area is that of a sector less the triangle, so the computation is the same either way.
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<h3>3/4 circle area</h3>
The area of a circle is given by ...
A = πr²
so 3/4 of a circle is 3/4 this value:
3/4 circle area = (3/4)(π)(10²) = 75π . . . . square units
<h3>Triangle area</h3>
The area of the isosceles right triangle is given by ...
A = 1/2s²
A = 1/2(10²) = 50 . . . . square units
<h3>Shaded area</h3>
The shaded area is the sum of these two ...
shaded area = 3/4 circle area + right triangle area
shaded area = 75π + 50 ≈ 285.6 . . . . square units
Answer:
12.6 miles I think. I would wait for another answer to be possitive.
