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COnsider a string of lngth 10 containing only 0 and 1

the number of strings containg exactly 3 0's or 3 1's is ____________

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Given we have strings of  only 0's and 1's..

Hence if we have exactly 3 0's , we will have 7 1's and if we have 3 1's , we have 7 0's..

As it is clear  having exactly 3 0's and exactly 3 1's not possible at the same time bcoz that would lead to length = 6 ..

Hence n(A ∩ B)   =   0 here as they are mutually exclusive things.

Hence  n(A U B)    =   n(A)  + n(B)  -  n(A ∩ B)

                            =  n(A)  +  n(B)

Now n(A)  : For that we need to select 3 0's out of 10 letters and the rest will be automatically 1's.                                           Hence number of ways   =    10C3   =   (10 * 9 * 8) / 6  =  120

Similarly n(B)   =   120

Hence n(A U  B)    =   240

Hence the required number of ways   =   240

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