A box contains 2 white balls, 3 black balls, and 4 red balls. The number of ways three balls can be drawn from the box if at least one black ball is to be included in the draw is ______.

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Payal Gupta | Contributor-Level 10

3 months ago

This is a Fill in the blanks Type Questions as classified in NCERT Exemplar

$\begin{array}{l} W e h a v e 2 w h i t e, 3 b l a c k a n d 4 r e d b a l l s \\ I t i s g i v e n t h a t a t l e a s t 1 b l a c k b a l l i s t o b e i n c l u d e d . \\ ∴ Required n u m b e r o f w a y s = {}_{3}{C_{1}} \times {}_{6}{C_{2}} + {}_{3}{C_{2}} \times {}_{6}{C_{1}} + {}_{3}{C_{3}} \\ = 3 \times 15 + 3 \times 6 + 1 = 45 + 18 + 1 = 64 \\ H e n c e, t h e v a l u e o f t h e f i l l e r i s 64 . \end{array}$

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A box contains 2 white balls, 3 black balls, and 4 red balls. The number of ways three balls can be drawn from the box if at least one black ball is to be included in the draw is ______.

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