math

in how many ways can 8 person be seated in a sofa if only 6 person can fit on it?

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  1. permutations of 8 taken 6 at a time
    (assuming that seating order on the sofa matters)
    = n!/(n-r)! = 8!/2!
    = 8*7*6*5*4*3
    but
    if seating order on the sofa does not matter then combinations of 8 taken 6 at a time
    = n!/[ (n-r)! r! ]

    = 8!/{2!*6!] = 8*7/2 = 4*7 = 28

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