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.
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