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NCERT Class XI Mathematics - Permutations and Combinations - Solutions

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Question : 29 of 41
Marks: +1, -0
A bag contains 5 black and 6 red balls. Determine the number of ways in which 2 black and 3 red balls can be selected.
Solution:  
No. of ways of selecting 2 black balls =  5C2\,{}^{5}C_2
No. of ways of selecting 3 red balls =  6C3\,{}^{6}C_3
∴ Required no. of ways of selecting 2 black & 3 red balls =  5C2\,{}^{5}C_2 ×  6C3\,{}^{6}C_3
= 5!2!3!×6!3!3!\frac{5!}{2!3!} \times \frac{6!}{3!3!} = 5×42×6×5×43×2\frac{5 \times 4}{2} \times \frac{6 \times 5 \times 4}{3 \times 2} = 200
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