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Question Number 106792 by bobhans last updated on 07/Aug/20

$$\succ \mathrm{bobhans}\prec$$$$\mathrm{From}\mathrm{a}\mathrm{batch}\mathrm{containing}6\mathrm{boys}\mathrm{and}4\mathrm{girls}$$$$\mathrm{a}\mathrm{group}\mathrm{of}4\mathrm{students}\mathrm{is}\mathrm{tobe}\mathrm{selected}.$$$$\mathrm{How}\mathrm{many}\mathrm{group}\mathrm{formations}\mathrm{will}\mathrm{have}$$$$\mathrm{exactly}2\mathrm{girls}?$$

Answered by bemath last updated on 07/Aug/20

$${}^{@\mathrm{bemath}@}$$$$\mathrm{Choose}2\mathrm{girls}\mathrm{out}\mathrm{of}4\mathrm{girls}\mathrm{total}\mathrm{and}2\mathrm{boys}\mathrm{out}\mathrm{of}6\mathrm{total}$$$$\mathrm{so}\mathrm{we}\mathrm{have}={\mathrm{C}}_2^4\times {\mathrm{C}}_2^6=\frac{4\times 3}{2\times 1}\times \frac{6\times 5}{2\times 1}$$$$=6\times 15=90\mathrm{groups}$$

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