A box contains 12 balls out of which 4 are red and rest are blue. In how many ways can a random sample of 5 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 5 balls of the same colour?

⁴C₂x ⁸C₃+ ⁴C₁x ⁸C₄

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⁴C₁x ¹¹C₄+ ⁴C₁x ⁸C₄

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⁴C₂x ¹⁰C₂+ ⁴C₁x ¹⁸C₅

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¹²C₅

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None of these

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Solution

The correct option is A
⁴C₂x ⁸C₃+ ⁴C₁x ⁸C₄

The number of ways that it can be done = $^{4} C_{2} \times^{8} C_{3}$ + $^{4} C_{1} \times^{8} C_{4}$

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A box contains 12 balls out of which 4 are red and rest are blue. In how many ways can a random sample of 5 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 5 balls of the same colour?

The correct option is A 4C2 x 8C3 + 4C1 x 8C4 The number of ways that it can be done = 4C2×8C3+4C1×8C4

The correct option is A
⁴C₂x ⁸C₃+ ⁴C₁x ⁸C₄

The number of ways that it can be done = $^{4} C_{2} \times^{8} C_{3}$ + $^{4} C_{1} \times^{8} C_{4}$