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Q.
Out of $ 6 $ boys and $ 4 $ girls, a group of $ 7 $ is to be formed. In how many ways can this be done, if the group is to have a majority of boys?
Jharkhand CECEJharkhand CECE 2008
Solution:
The boys in majority, if boys are more than girls. The boys are in majority, if the groups are
$ 4B\,\,3G,\,\,5B\,\,2G,\,\,6B\,\,1G $ .
Total number of combinations
$ {{=}^{6}}{{C}_{4}}{{\times }^{4}}{{C}_{3}}{{+}^{6}}{{C}_{5}}{{\times }^{4}}{{C}_{2}}{{+}^{6}}{{C}_{6}}{{\times }^{4}}{{C}_{1}} $
$ =15\times 4+6\times 6+1\times 4 $
$ =60+36+4=100 $