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A box contains $10$ balls out of which $3$ are red and rest are blue.

In how many ways can a random sample of $6$ balls be drawn from the bag so that at the most $2$ red balls are included in the sample and no sample has all the $6$ balls of the same colour?









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Option(B) is correct

Six balls can be selected in the following ways:

One red ball and 5 blue ball

Two red balls and 4 blue balls

Total number of ways:
$= ({^3C_1} × {^7C_5}) + ({^3C_2} × {^7C_4})$

$= 63 + 105$

$= \textbf{168}$

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