Tim and Stacy need to select seats in a row of chairs that are numbere

Question

Tim and Stacy need to select seats in a row of chairs that are numbered in order from 1 to 5. If Tim cannot sit in an even-numbered seat and Stacy cannot sit in an odd-numbered seat, how many arrangements are possible if the two cannot sit adjacent to each other and Tim and Stacy are the only people to be seated?

A. 1
B. 2
C. 3
D. 5
E. 20

A. 1
B. 2
C. 3
D. 5
E. 20

KarishmaB · Accepted Answer

Another method:

Tim occupies only an odd numbered seat so three options (1, 3, 5)
Stacy occupies only an even numbered seat so two options (2, 4)

If Stacy sits on seat 2, Tim must be on seat 5. (Tim cannot be on seats 1 or 3 because he will be right next to Stacy in those cases)
If Stacy sits on seat 4, Tim must be on seat 1.

These 2 are the only possible options.

Answer (B)

Divyadisha · Answer

Is the answer 'b' i.e. 2?

The total number if there is no restriction is = 2X3= 6
and if both are sitting together, the combination is = 2X2= 4

So, the way they can not sit together is 6-4=2

nipunjain14 · Answer

Tim can sit on seats 1, 3 5
Stacey can sit on 2 or 4
but both cant sit adjacent, thus if stacey sits on 2 then tim will have to sit on 5 
if stacey sits of 4 then tim needs to sit on 1

only 2 arrangements possible

Thus ans: B

ramlala · Answer

Team's possibility of sitting is (1,3,5)
Stacey's possibility of sitting (2,4)

Combined 2 scenarios: (1,4) & (5,2)
other 4 scenarios ruled out: (1,2), (3,2), (3,4), (5,4)

Ans: B

SHYAM23 · Answer

5c2=10
5c3=10
cant we do it with combination method

Tonkotsu · Answer

I am not 100% certain, but I would gather no. 
When the problem says 'arrangement', usually that means that order matters so going with permutation seems to make more sense.

There should only be 2 choices since T and S cannot be next to each other.

bumpbot · Answer

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Tim and Stacy need to select seats in a row of chairs that are numbere

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Tim and Stacy need to select seats in a row of chairs that are numbere

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