There are 5 chairs. Bob and Rachel want to sit such that Bob is always left to Rachel. How many ways it can be
done?
done?
Regards,
Sach
Sach
The question seems to be asking:
How many ways can Bob and Rachel be seated in a row of 5 chairs if Bob must sit to the left of Rachel and the other 3 chairs are to remain empty?
TOTAL WAYS to arrange Bob and Rachel in the 5 chairs:
Number of options for Bob = 5. (Any of the 5 chairs.)
Number of options for Rachel = 4. (Any of the 4 remaining chairs.)
To combine these options, we multiply:
5*4 = 20.
Total ways to seat Bob TO THE LEFT of Rachel:
In half of the 20 arrangements counted above, Bob will be to the left of Rachel; in the other half, Rachel will be to the left of Bob.
Thus, we divide by 2:
20/2 = 10.
Another option is to write out the acceptable arrangements.
Let B = Bob, R = Rachel, X = an empty chair.
Here are all of the acceptable arrangements:
BRXXX
BXRXX
BXXRX
BXXXR
XBRXX
XBXRX
XBXXR
XXBRX
XXBXR
XXXBR
Total ways = 10.
