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.
-------------------------------
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 :)
<em><u>Problem One</u></em>
Remark
You don't pay a sales tax until cash is exchanged for goods or services.
So what is 70% off
Solution
Sale price = given price * (100% - 70%)
Sale Price = 72 * 30%
Sale Price = 72 * 30/100
Sale Price = 72 * 0.3
Sale Price = 21.6 dollars.
The sales tax is 5% of this amount
21.6 * 5/100 = 1.08
The total cost is = 21.6 + 1.08 = 22.68
Problem Two
If they marked up 100%, effectively they doubled the price.
New Price = old price + 100% of old price.
New Price = 48.50 + 48.50 = 97 dollars.
The sales tax is 6% * 97 = 6/100 * 97 = 5.82
Total Cost = Cost of item + Tax
Total Cost =97 + 5.82
Total Cost = 102.82 Answer <<<<
5% = 0.5
0.5n = 85
Divide by 0.5
0.5n = 85
/0.5 /0.5
n = 170.
The number is 170.
I will do my best to explain this “ x method “ I use
Basically, two factors of the first and last number must multiply together to sum up to equal the middle number
1 X 12
1 4
(x+12) (x+4)
Hope this helps!
