2) In how many ways could 10 people be seated at a rectangular table if the two hosts should not sit together?
Answers
Solution
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Correct option is A)
Step 1: Use combination, permutation to find the number of ways
Total number of ways of selecting 3 people out of 10 people =
10
C
3
Total number of ways in which all are consecutive =10
Total number of ways in which only two persons are adjacent to each other =10×6
and other is apart =60
Required number of ways =
10
C
3
−10−60
=
3!×7!
10!
−70
=
3×2
10×9×8
−70
=120−70
=50
Hence, the required number of ways is 50