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2 years ago

Evaluate: a) n!/(n-3)!b) P(6,4)/4!

Mathematics

1 answer:

telo118 [61]2 years ago

3 0

Step-by-step explanation:

a).

n! is

$n(n - 1)(n - 2)(n - 3)(n - 4).........(1)$

(n-3)! is

$(n - 3)(n - 4)(n - 5)..........(1)$

If we divide the two, everything behind (n-3) will just cancel out so we would be left with only

$(n)(n - 1)(n - 2)$

So the answer to a is

$n(n - 1)(n - 2)$

Permutations formula of P(6,4) is

6!/(6-4)!, or 6!/2!.

$\frac{6 \times 5 \times 4 \times 3 \times 2 \times 1}{2 \times 1} = 360$

Then we divide by 4!

$\frac{360}{4 \times 3 \times 2 \times 1} = 15$

The answer to b is 15

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Select the point that is a solution to the system of inequalities.<br> y≤2x-2<br> y≤ x²-3x

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Both statements are true. Therefore (4,2) is a solution and option D is correct.

The given inequalities are $y\leq 2x-2$ and $y\leq x^{2} -3x$ .

We need to select the point that is a solution to the system of inequalities (-2,-1), (1,3), (2,1) and (4,2).

<h3>What is an example of a system of inequalities in real life?</h3>

Inequalities can be seen in the speed limits on roads, the minimum age for seeing certain movies, and the distance you have to walk to go to the park. Inequalities represent a limit of what is permitted or achievable rather than a precise quantity.

Any point is a solution to this system of inequality if it satisfies both inequalities.

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For (1, 3), $3\leq 2(1)-2 \implies 3\leq 0$

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For (2,1), $1\leq 2(2)-2 \implies 1\leq 2$ .

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Both statements are true. Therefore (4,2) is a solution and option D is correct.

To learn more about inequalities visit:

brainly.com/question/20383699.

#SPJ1

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2 years ago

Evaluate: a) n!/(n-3)!b) P(6,4)/4!​

Evaluate: a) n!/(n-3)!b) P(6,4)/4!