27. Find the number of ways of selecting 9 balls from 6 red balls, 5 white balls and 5blue balls if each selection consists of 3 balls of each colour.

27. Since we are to select 3 balls from each colour in order to select 9 balls from the collections of 6, 5 and 5 balls of red, white and blue colours respectively, we can have the combination

⁶C₃ (red) ×⁵C₃ (white) ×⁵C₃ (blue)

= $\frac{6!}{3!\left(6-3\right)!}$ × $\frac{5!}{3!\left(5-3\right)!}$ × $\frac{5!}{3!\left(5-3\right)!}$

= 20 × 10 × 10

= 2000

<p><strong>27.</strong> Since we are to select 3 balls from each colour in order to select 9 balls from the collections of 6, 5 and 5 balls of red, white and blue colours respectively, we can have the combination</p><p>⁶C₃ (red) ×⁵C₃ (white) ×⁵C₃ (blue)</p><p>=&nbsp;<span title="Click to copy mathml"><math><mrow><mfrac><mrow><mn>6</mn><mo>!</mo></mrow><mrow><mn>3</mn><mo>!</mo><mrow><mo> (</mo><mrow><mn>6</mn><mo>−</mo><mn>3</mn></mrow><mo>)</mo></mrow><mo>!</mo></mrow></mfrac></mrow></math></span>&nbsp;×&nbsp;<span title="Click to copy mathml"><math><mrow><mfrac><mrow><mn>5</mn><mo>!</mo></mrow><mrow><mn>3</mn><mo>!</mo><mrow><mo> (</mo><mrow><mn>5</mn><mo>−</mo><mn>3</mn></mrow><mo>)</mo></mrow><mo>!</mo></mrow></mfrac></mrow></math></span>&nbsp;×&nbsp;<span title="Click to copy mathml"><math><mrow><mfrac><mrow><mn>5</mn><mo>!</mo></mrow><mrow><mn>3</mn><mo>!</mo><mrow><mo> (</mo><mrow><mn>5</mn><mo>−</mo><mn>3</mn></mrow><mo>)</mo></mrow><mo>!</mo></mrow></mfrac></mrow></math></span></p><div><div><picture><source srcset="" media=" (max-width: 500px)"><img src="https://images.shiksha.com/mediadata/images/1747819378phpzVdJ0J.jpeg" alt="" width="290" height="51" loading="lazy"></picture></div></div><p>= 20 × 10 × 10</p><p>= 2000</p>

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