Asked by rona
in how many ways can 8 person be seated in a sofa if only 6 person can fit on it?
Answers
Answered by
Damon
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
(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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