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True-or-False:There will be only at 24 selections containing atleast one red ball out of a bag containing 4 red and 5 black balls.It is being given that balls of the same colour are identical.

$\begin{array}{1 1}(A)\;\text{True}\\(B)\;\text{False}\end{array} $

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A)
9C0+9C1+......+9C9 gives all possible selections. In these sections we look for selections with at least one red ball. r=1 section R is in 1 way r=2 sections RR , RB are in 2 way. r=3 sections RRR , RRB, RBB are in 3 ways. r=4 sections RRRR , RRRB , RRBB, RBBB are in 4 ways r=5 sections RRRRB , RRRBB, RRBBB, RBBBB are in 4 ways r=6 sections RRRRBB , RRRBBB, RRBBBB, RBBBBB are in 4 ways. r=7 sections RRRRBBB, RRRBBBB , RRBBBBB are in 3ways. r=8 sections RRRRBBBB , RRRBBBBB are in 2 ways r=9 section of all balls is in 1 way Total=24 ways of selecting at least one red ball.
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