Student
64 Points
Joined May 2012
Lets say we have 5 items - Sample Space = [B1, B2, B3, B4, B5]
From this we are selecting 2 with replacement. Lets say we are selecting B1 first. Now the sample space would be [B2,B3,B4,B5]. B1 in our hand. We are selecting with replacement. Hence we keep the item B1 back into the sample space. Now the sample space is [B1, B2, B3, B4, B5]. Now select the 2nd item which could be either B1, or B2 or B3 or B4 or B5. ie the pair of items selected would be
(B1,B1) , (B1,B2) , (B1,B3) , (B1,B4) , (B1,B5) - 5 ways of selecting.
Now the same could be applied with selecting B2 as the first item.
(B2,B1) , (B2,B2) , (B2,B3) , (B2,B4) , (B2,B5) - 5 ways of selecting.
Likewise for B3,B4 and B5.
(B3,B1) , (B3,B2) , (B3,B3) , (B3,B4) , (B3,B5) - 5 ways of selecting.
(B4,B1) , (B4,B2) , (B4,B3) , (B4,B4) , (B4,B5) - 5 ways of selecting.
(B5,B1) , (B5,B2) , (B5,B3) , (B5,B4) , (B5,B5) - 5 ways of selecting.
Thus the total ways of selecting 2 items from 5 items with replacement is 25. It is generally given by the formula N^n.
N- Total size and n - sample size.
Hope the explanation is clear. Thanks.