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NCERT Class XI Mathematics - Permutations and Combinations - Solutions

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Question : 26 of 41
Marks: +1, -0
Find the number of ways of selecting 9 balls from 6 red balls, 5 white balls and 5 blue balls if each selection consists of 3 balls of each colour.
Solution:  
No. of ways of selecting 3 red balls =  6C3\,{}^{6}C_3
No. of ways of selecting 3 white balls =  5C3\,{}^{5}C_3
No. of ways of selecting 3 blue balls =  5C3\,{}^{5}C_3
∴ Required no. of ways of selecting 9 balls
=  6C3\,{}^{6}C_3 ×  5C3\,{}^{5}C_3 ×  5C3\,{}^{5}C_3 = 6!3!3!×5!32!×5!3!2!\frac{6!}{3!3!} \times \frac{5!}{32!} \times \frac{5!}{3!2!} = 6×5×43×2×5×42×5×42\frac{6\times5\times4}{3\times2} \times \frac{5\times4}{2} \times \frac{5\times4}{2} = 2000.
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