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Feliz [49]
3 years ago
5

Is this problem a combination or permutation?

Mathematics
2 answers:
Morgarella [4.7K]3 years ago
5 0

Answer:

Combination

Step-by-step explanation:

This is the answer because:

1) The difference between combinations and permutations is the ordering of each term.

Combinations - the order doesn't matter

Permutations - the order matters.

An example of this is, if you enter the number combination 5324 into your locker/cabinet, it won't open up because it is a different ordering and needs a specific combination which means it's permutation.  

2) In this situation, the order doesn't not matter since they just want different ways to select an assistant, a representative, a treasurer, and a recorder.

Hope this helps! :D

HACTEHA [7]3 years ago
4 0

Answer: Permutation Problem

There are 5040 permutations possible

==================================================

Explanation:

Order matters because the positions are different.

(A,B,C,D) is different from (B,A,C,D) because the first means person A is the assistant while the second means person B is the assistant.

We have 10 choices for the first slot, 9 for the second, 8 for the third, and 7 for the fourth. We count down the values because a person cannot be reselected to serve multiple positions simultaneously.

Multiply out those values to get 10*9*8*7 = 5040

There are 5040 permutations possible.

---------------

As an alternative, you can use the nPr permutation formula with n = 10 and r = 4 like so

_n P_r = \frac{n!}{(n-r)!}\\\\_{10} P_{4} = \frac{10!}{(10-4)!}\\\\_{10} P_{4} = \frac{10!}{6!}\\\\_{10} P_{4} = \frac{10*9*8*7*6!}{6!}\\\\_{10} P_{4} = 10*9*8*7 \ \ \text{ ... note how this shows up again}\\\\_{10} P_{4} = 5040\\\\

We get the same answer as before.

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Answers

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Step-by-step explanation:

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3 years ago
Forces of 9 lbs and 13 lbs act at a 38º angle to each other. Find the magnitude of the resultant force and the angle that the re
fiasKO [112]

Answer: R=20.84\ lb\quad 22.57^{\circ},15.43^{\circ}

Step-by-step explanation:

Given

Two forces of 9 and 13 lbs acts 38^{\circ} angle to each other

The resultant of the two forces is given by

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\Rightarrow R=\sqrt{9^2+13^2+2(9)(13)\cos 38^{\circ}}\\\Rightarrow R=\sqrt{81+169+184.394}\\\Rightarrow R=\sqrt{434.394}\\\Rightarrow R=20.84\ lb

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\Rightarrow \alpha=\tan^{-1}\left( \dfrac{b\sin \theta}{a+b\cos \theta}\right)\\\\\text{Considering 9 lb force along the x-axis}\\\\\Rightarrow \alpha =\tan^{-1}\left( \dfrac{13\sin 38^{\circ}}{9+13\cos 38^{\circ}}\right)\\\\\Rightarrow \alpha =\tan^{-1}(\dfrac{8}{19.244})\\\\\Rightarrow \alpha=22.57^{\circ}

So, the resultant makes an angle of 22.57^{\circ} with 9 lb force

Angle made with 13 lb force is 38^{\circ}-22.57^{\circ}=15.43^{\circ}

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Answer:

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