Jake, Lena, Fred, John and Inna need to drive home from a party in a car that can seat 7 people. If only Inna or Jake can drive, how many seat allocations are possible?
a. 30
b. 42
c. 60
d. 120
e. 125
Permutation and Combination Question
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30
30
I agree with Jay. The answer is 30.
Please some body figure it out and explain the logic for the answer being 30.
Because i am struck in the middle, i arrived at 42 but after subtracting the combination for the driver seat , is it 30?
Please explain!!
well guys…according to the source…the correct answer is 60…
can anyone explain y is it so?
Illusions you are right its 60 because if Jake is driving
then the Inna is not so one seat is taken. The rest can
be arranged in 6 diff ways. Now if Inna is driving
the the same holds so 6!/4!+6!/4! = 60.
If Jake is driving that the remaining 6 seats can be used to seat 4 people thts 6C4 ways=30.
Same holds true if Inna is driving.i.e 6C4 ways=30
So 30+30=60 ways
The answer choices provided with this problem are incorrect.
If Jake is driving, then there are six seats remaining, to be filled with the following values:
Lena–Fred–John–Inna–[empty]–[empty]
or
LFJIEE
The order matters here, but not the order of the two empty seats, so use the formula for permutation w/ repeating elements, to get:
6! / 2! = 360
If Inna is driving, the same number of possibilities exist as described above, with Jake taking Inna’s spot in each of the arrangements. So the answer to the question is 2*360=720.
I should point out that this, and many of the questions on this site, are copyrighted material and should not be reproduced without the permission of the original authors. As you may know, scoretop.com was recently shut down for exactly such violations (as well as suspicion of showing LIVE test problems!).
Here is another site (improperly) posting this problem, but with the correct answer choices (and a link to an explanatory solution)
The least a person posting questions can do is put up the right answer choices!!!
I came up with 720 and finding no match was quite frustrated as is the right solution!!
This site has lost some credibility for me!
60
Ans choices are incorrect
this is an arrangement.
P(6,4) * 2 = 710
Susan loosing temper or getting frustrated is not a sign for a good executive (:))
I go with vijay but it is not 6C4 it is 6P4=30
it is obvious it is 720 since not considering driver you have 4 people in 6 seats so it is 6!/2! per each driver. since you have two drivers you have a total of 6! permutations
Answer is 120::::::::5!