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 :)
She needs to score a 91 on her next test because 85+78+77+69+91=400 and 400 divided by 5 gives you a mean of 80.
I believe the answer would be B. money market funds.
Is it a multiple choice question?
The value of the <em>a, </em>in the provided quadratic equation for which Nancy found one solution as x=1 is 9.
<h3>What is the solution of equation?</h3>
The solution of the quadratic equation is the solution of the variable of the equation, for which the equation satisfies.
Nancy found that x=1 is one solution to the quadratic equation. The quadratic equation is,
For this equation, one solution is <em>x</em>=1. Put this value in the above equation to get the value of <em>a,</em>
Thus, the value of the <em>a, </em>in the provided quadratic equation for which Nancy found one solution as x=1 is 9.
Learn more about the solution of the equation here;
brainly.com/question/21283540
