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PERMUTATIONS

PERMUTATIONS

by Chandni Bhatia -
Number of replies: 2

Q.1}If r>p>q,the number of differnt selections of p+q things taking r at a time,wheer p things are identical and other q things are identical, is

[a] p+q-r   [b] p=q-r=1   [c] r-p-q+1    [d] none of these 

Q.2}A bag contains 3 black,4 white and 2 red balls,all the balls being different.The number of selections of at most 6 balls containing balls of the colours is

[a] 42*{4}! [b]26*{4}!  [c] (26-1){4}!  [d] none of these

In reply to Chandni Bhatia

Re: Combinations

by Manish Verma -
Q1 looks like application of the following:

When there are n things, out of which p things are alike and q things are alike (but different from p things) and so on and r things have to be selected from n things, then the number of ways =
coeff. of xr in (x0+x1+x2+.........+xp)(x0+x1+x2+.........+xq).............

n can be equal to p+q and if so, it should just be
coeff. of xr in (x0+x1+x2+.........+xp)(x0+x1+x2+.........+xq)

Q2: Something is missing from the second sentence.
In reply to Manish Verma

Re: Combinations

by Chandni Bhatia -
Sir,as far as second question is concerned I have checked it from the book.Same thing is written there.May be something is wrong in the book.  Can you please explain the logic for first question?