Wednesday, November 24, 2010

How many ways are there of choosing objects without replacement ?

How many ways are there of choosing 6 objects, without replacement, from 14 distinct objects, if



the order of the choices is not taken into consideration?

the order of the choices is taken into consideration?



please explain to me , thank youHow many ways are there of choosing objects without replacement ?let us look first at the second case



the order of the choices is taken into consideration?



for the first choice you have 14 choices, then the second choice 13, then 12



so it works out as 14 x 13 x 12 x 11 x 10 x 9 = 2 162 160



in the second case

the order of the choices is not taken into consideration?



here it is the same as above, but the order could have been in 6x5x4x3x2x1 different ways



so it works out as 14 x 13 x 12 x 11 x 10 x 9 / (6x5x4x3x2x1 ) = 3003How many ways are there of choosing objects without replacement ?If there are 14 objects laid in front of you and you take 6, that leaves 8 objects in front of you. Without replacement, you remove another 6 objects from the 8 remaining, that leaves 2 left over. So there are only 2 ways, without replacement, of choosing 6 objects.
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